The values of  $\theta$ satisfying  $\sin 5\theta =\sin 3\theta -\sin \theta$and  $0<\theta <\frac{\pi }{2}$ are

$\sin 5\theta =\sin 3\theta -\sin \theta$ $0\le \theta <\frac{\pi }{2}$

$\sin 5\theta +\sin \theta =\sin 3\theta$

$2\sin 3\theta \cos 2\theta =\sin 3\theta$

$\sin 3\theta (2\cos 2\theta -1)=0$

$\sin 3\theta =0,2\cos 2\theta =1$

$3\theta =n\pi$ (or) $\text{cos}2\theta =\cos 60°$

$\theta =\frac{n\pi }{3}$ (or) $2\theta =2n\pi \pm \frac{\pi }{3}$

$\theta =n\pi \pm \frac{\pi }{6}$

$\text{0}<\theta <\frac{\pi }{2},\theta =\frac{\pi }{6}\text{,}\frac{\pi }{3}$