A gyro is not the way to go for this. Specific to the L3DG20 is reports a "Digital zero rate level" of 10 degrees/second; that's the inaccuracy of the device when it's just sitting at rest, reporting up to 10 degrees/second of movement. This inaccuracy is typical for any mems gyro.
What you would need to use is a rotary encoder, but you're asking for one with 360,000 counts per revolution. For something with that accuracy I think you'd have to steal one from an observatory with a high power telescope.