RACK AND PINION VARIABLE VANE SYNCHRONIZING MECHANISM FOR INNER DIAMETER VANE SHROUD This invention was made with U.S. Government support under contract number N00019-02-C-3003 awarded by the United States Navy, and the U.S. Government may have certain rights in the invention. CROSS-REFERENCE TO RELATED APPLICATION^) The present application is related to the following copending applications filed on the same day as this application: "SYNCH RING VARIABLE VANE SYNCHRONIZING MECHANISM FOR INNER DIAMETER VANE SHROUD" by inventors J. Giaimo and J. Tirone in (attorney docket number U73.12-003); "OEAR TRAIN VARIABLE VANE SYNCHRONIZING MECHANISM FOR INNER DIAMETER VANE SHROUD" by inventors J. Giaimo and J. Tirone m (attorney docket number U73.12-004); "INNER DIAMETER VARIABLE VANE ACTUATION MECHANISM" by inventors 'J. Giaimo and J. Tirone III (attorney docket number U73.12-005); and "LIGHTWEIGHT CAST INNER DIAMETER VANE SHROUD FOR VARIABLE STATOR VANES" by inventors J. Giaimo and J. Tirone HI (attorney docket number U73.I2-006). All of these applications are incorporated herein by this reference. B ACKGROUNP OF THE INVENTION This invention relates generally to gas turbine engines and more particularly to variable stator vane assemblies for use in such engines. Gas turbine engines operate by combusting a fuel source in compressed air to create heated gases with increased pressure and density. The heated gases are ultimately forced through an exhaust nozzle, which is used to step up the velocity of the exiting gases and in-torn produce thrust for driving an aircraft. The heated gases are also used to drive a turbine for rotating a fan to provide air to a compressor section of the gas turbine engine. Additionally, the heated gases are used to drive a turbine for driving rotor blades inside the compressor section, which provides the compressed air used during combustion. The compressor section of a gas turbine engine typically comprises a series of rotor blade and stator vane stages. At each stage, rotating blades push air past the stationary vanes. Each rotor/stator stage increases the pressure and density of the air. Stators serve two purposes: they convert the kinetic energy of the air into pressure, and they redirect the trajectory of the air coming off the rotors for flow into the next compressor stage. Hie speed range of an aircraft powered by a gas turbine engine is directly related to the level of air pressure generated in the compressor section. For different aircraft speeds, the velocity of the airflow through the gas turbine engine varies. Thus, the incidence of the air onto rotor blades of subsequent compressor stages differs at different aircraft speeds. One way of achieving more efficient performance of the gas turbine engine over the entire speed range, especially at high speed/high pressure ranges, is to use variable stator vanes which can optimize the incidence of the airflow onto subsequent compressor stage rotors. Variable slater vanes are typically circumferenUaJly arranged between an outer diameter fan case and an inner diameter vane shroud. Traditionally, mechanisms coordinating the synchronized movement of the variable stator vanes have been located on the oulside of the fan case. These systems increase the overall diameter of the compressor section, which is not always desirable or permissible. Also, retrofitting gas turbine engines that use stationary stator vanes for use with variable stator vanes is not always possible. Retrofit variable vane mechanisms positioned outside of the fan case interfere with other external components of the gas turbine engine located on the outside of the fan case. Relocating these other external components is often impossible or too costly. Synchronizing mechanisms also add considerable weight to the gas turbine engine. Thus, there is a need for a lightweight variable vane synchronizing mechanism that does not increase the diameter of the compressor section and does not interfere with other external components of the gas turbine engine. BRIEF SUMMARY OF THE INVENTION In the present invention, an inner diameter vane shroud accommodates a synchronizing mechanism for coordinating rotation-of an array of variable vanes. The inner diameter vane shroud has a gear track that runs circamferentiatly through the vane shroud. An array of variable vanes is rotatably mounted in the vane shroud at an inner end. Bach variable vane includes a gear pinion at its inner end, which interfaces with the gear track. As one of the individual variable vanes is rotated by an actuation source, the other variable vanes of the variable vane array are rotated a like amount by the rack and pinion gear interface. BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 shows a partially cut away front view of a staler vane section of a gas turbine engine in which the present invention is used. FIG. 2A shows a front view of a segment of the staior vane section of FIG. 1 between arrows A and C, with the inner diameter vane shroud removed between arrows B and C and the fan case removed. FIG. 2B shows a partially cut away front view of a segment of the inner diameter vane shroud between arrows A and B of FIG. 1. FIG. 3A shows a close-up of the rack and pinion mechanism of the present invention shown from the vantage of line D