Answer
$-\csc \sqrt\theta\cot \sqrt\theta-\ln|\csc \sqrt\theta+\cot\sqrt\theta|+C$
Work Step by Step
Suppose $u=\sqrt\theta \implies du=\dfrac{1}{2\sqrt\theta}d\theta $
Let $I=2(-\dfrac{\csc u \space \cot u}{2}+*(1/2) \space \int\csc udu)\\=-\csc u \space \cot u+\int\csc (u) du \\=-\csc u\cot u-\ln|\csc u+\cot u|+C\\=-\csc \sqrt\theta\cot \sqrt\theta-\ln|\csc \sqrt\theta+\cot\sqrt\theta|+C$
