$\int_{0}^{\pi/2} \frac{\arctan^2 \left ( \sin^2 x \right )}{\sin^2 x} \, {\rm d}x$

Question

Does anyone have any ideas on how to attack this:

$$\int_{0}^{\pi/2} \frac{\arctan^2 \left ( \sin^2 x \right )}{\sin^2 x} \, {\rm d}x$$

I cannot think of something that could work. Wolfram Alpha does not evaluate it either.