I'm using x instead of theta (same difference)
2cosx - sin 2x = 0
2cos x - 2sinx cosx = 0 factor
2cos x ( 1 - sinx ) = 0 set each factor to 0 and solve
2cos x = 0 divide through by 2 1 - sin x = 0
cos x = 0 sin x = 1
x = 90°, 270° x = 90°
So x = 90° , 270°