$\int_{0}^{\pi/2}{\frac{dx}{a+\sin^2(x)}}$ for $|a|>1$

Question

Evaluate: $$\int_{0}^{\pi/2}{\frac{dx}{a+\sin^2(x)}}$$ for $|a|>1$

Note: This integral is to be solved using complex analysis (Calculus of Residues)