\tan(2\Delta\theta) = \frac{D_1\sin(2\theta_2)-D_2\sin(2\theta_1)}{D_2\cos(2\theta_1)-D_1\cos(2\theta_2)}

\)

I want to have an expression for delta theta. I know i can just take arctan for both sides, but i want right side part to be more simple because it would be computed often. Thanks.