5.625 = 360 / 64, ie, there are 64 steps per revolution.
However, the actual number of steps can be some multiple of that, depending on how you energize the windings. 2 to 4 times that number is easily achieved, and microstepping drivers can provide substantially finer interpolated resolution.
Your specification is not very clear - you seem to say both 2 degree steps, and 2 degree accuracy. Probably you want 2 degree steps with an accuracy of some fraction of that.
64 steps is relatively course - 200 step motors are widely available.
If you are looking at mechanical reduction, consider toothed timing belts and sprockets instead of gears. They are have less critical needs for mechanical alignment, and run quieter. If your system must operate in both directions without slop, the fact that timing belts suffer minimal backlash when the direction of torque is reversed makes them strongly preferable versus gears.