Answer
$-\dfrac{\csc \theta}{2}+C$
Work Step by Step
Given: $\int (\dfrac{1}{2} \csc \theta \cot \theta) d\theta$
Thus, $\int (\dfrac{1}{2} \csc \theta \cot \theta) d\theta= \dfrac{1}{2}\int ( \csc \theta \cot \theta) d\theta=-\dfrac{\csc \theta}{2}+C$