I have this circuit using TL064IN OPAMP to amplify a 50Hz signal two times with different gains, the two output signals has to be in phase with each other. The problem is when I did the simulation to figure out the phase shift between two signals and then try to compensate for this phase shift by using capacitors, the LT spice simulation gave me a 38 mili degree when using the capacitors shown on the schematic. But in reality the phase is more than that. Is there any way to know the real phase shift and find the exact values for the capacitors other than try and error? the graph of Gain VS frequency vs phase is not very useful for accurate calculation.
First things first. You need to stop asking for insane levels of accuracy. Sure, your Spice package gives phase measurements with a resolution of 0.9 micro-degree, and group delay resolution of 1 psec. Do not pay attention to this. When measuring 50 Hz phase, for instance, your 38 mdeg corresponds to 2 usec. Do you really care about microsecond differences? If so, why? And consider that your real-life components will probably be 1% resistors and 10% capacitors, so the equations which produced the numbers really cannot be used at this level of accuracy.
With that in mind, tell us a) what accuracy you need, and b) what accuracy you're getting. "more than that" is not remotely useful.