how to get the angle from a 3 phases synchro signal
There are several approaches, but all of them are based on converting the 3-phase signal to a 2-phase signal, with the amplitudes of the two signals proportional to the sine and cosine of the shaft angle. With the two amplitudes detected, the angle can be computed via the arctan function (paying due attention to polarities to get the quadrant right).

The transformation was originally performed using a Scott-T transformer (this was back in the days of vacuum tubes), but a pair of op amps will do the trick. See http://www.analog.com/media/en/technical-documentation/application-notes/50205505838923AN252.pdf for a detailed discussion, along with resistor values.

Briefly, the circuit looks like







simulate this circuit &ndash; Schematic created using CircuitLab

And the resistors are scaled to produce

SINE = C - A

COSINE = (2/sqrt 3)(B - A/2 - C/2)

Since different synchros use different voltages, you have to pick the appropriate scale factors suitable to your specific device.