Answer
$$ f'(\theta) =\cot \theta.$$
Work Step by Step
Recall that $(\ln x)'=\dfrac{1}{x}$
Recall that $(\sin x)'=\cos x$.
Since $ f(\theta)=\ln (\sin \theta)$, then the derivative, using the chain rule, is given by
$$ f'(\theta)=\frac{1}{\sin \theta}(\sin \theta)'=\frac{\cos \theta}{\sin\theta}=\cot \theta.$$
