This is the sequel of my previous [question](https://math.stackexchange.com/questions/172411/evaluating-int-0-infty-frac-arctan-sin2xxdx) 

$$I(a)=\int\_{0}^{\infty}\frac{\arctan (a\,\sin^2x)}{x^2}dx$$ I want to use differentiation under the integral sign with respect to parameter "a" but so far without success. 

Any hint?