Let $f(\theta)=\sin \theta(\sin \theta+\sin 3\theta)$.Then $f(\theta)$ is

Question

$$\begin{array}{1 1}a)\;\geq 0\;only\;when\;\theta\geq 0\\b)\;\leq 0\;for \;all\;real\;\theta\\c)\;\geq 0\;for\;all\;real\;\theta\\d)\;\leq 0\;only\;when\;\theta\leq 0\end {array}$$