A value of \(\theta\) satisfying \(\sin 5 \theta-\sin 3 \theta+\sin \theta=0\), such that \(0 < \theta < \frac{\pi}{2}\) is

Given expression
\[
\sin 5 \theta-\sin 3 \theta+\sin \theta=0 ; \theta \in(0, \pi / 2)
\]
\(\quad(\sin 5 \theta+\sin \theta)=\sin 3 \theta\) \(2 \cdot \sin 3 \theta \cdot \cos 2 \theta=\sin 3 \theta\) \(\Rightarrow \quad \sin 3 \theta(2 \cos 2 \theta-1)=0\) \(\Rightarrow \quad \sin 3 \theta=0\) and \(2 \cos 2 \theta=1\) \(\Rightarrow \quad \sin 3 \theta=\sin 0^{\circ}\) and \(\cos 2 \theta=1 / 2=\cos \pi / 3\) \(\Rightarrow \quad 3 \theta=0, \pi\) and \(2 \theta=\pi / 3\) \(\Rightarrow \quad \quad \theta=0, \pi / 3\) and \(\theta=\pi / 6\) So, the value of \(\theta\) satisfying given expression is \(\theta=\pi / 3, \pi / 6 .\) \(\theta=\pi / 3, \pi / 6\).