A Tricky Integral!!

Calculus Level 2

$\int _{ 0 }^{ { \pi } / { 2 } }{ \dfrac { \sqrt { \cot{x} } }{ \sqrt{\cot{x}}+ \sqrt{\tan{x}}}} \, dx = \, ?$

\frac{\pi}{4}

\frac{\pi}{2}

\pi

The integral diverges.