Actually you can use Euler's

(1) : sin(x)+sin(y) = 0.90154195

(2) : cos(x)+cos(y) = 1.64483049

(2) + i(1) : e^ix + e^iy = 1.64 + i0.90

(2) - i(1) : e^-ix + e^-iy = 1.64 - i0.90

Now use A = e^ix; B = e^iy.

A + B = 1.64 + i0.90

1/A + 1/B = 1.64 - i0.90

Solve this system.