We need to evaluate $\displaystyle \int_0^{\pi/2} {\sin^2x \over 1 + \sin x\cos x}dx$ and some solution to this starts as,
$\displaystyle\int_0^{\pi/2} {\sin^2x \over 1 + \sin x\cos x}dx = \int_0^{\pi/2} {\{\sin(\pi/2 -x)\}^2 \over 1 + \sin (\pi/2 -x)\cos (\pi/2 -x)}dx$.
We fail to understand how this step has been carried out. Even variable substitution does not seem to work.
Do you think that you could give us a hint?