Integral $\int_{0}^{\pi/2} \arctan \left(2\tan^{2}\left(x\right)\right) \mathrm{d}x$

The following integral may seem easy to evaluate ...

$$\int_{0}^{\pi/2}\arctan \left(2\tan^{2}\left(x\right)\right) \mathrm{d}x =\pi\arctan\left(\frac{1}{2}\right)$$Could you prove it ?.