The values of $\text{'}\theta \text{'}$ satisfying $\sin 7\theta =\sin 4\theta -\sin \theta \text{ in 0<}\theta <\frac{\pi }{2}$ are

$\begin{array}{l}\sin 7\theta =\sin 4\theta -\sin \theta \\ \Rightarrow \sin 7\theta +\sin \theta =\sin 4\theta \\ \Rightarrow 2\sin 4\theta .\cos 3\theta =\sin 4\theta \\ \sin 4\theta [2\cos 3\theta -1]=0\\ \sin 4\theta =0\text{ or}\cos 3\theta =\frac{1}{2}\end{array}$

$\begin{array}{l}\sin 4\theta =\sin \pi \text{ or }\cos 3\theta =\cos \frac{\pi }{3}\\ 4\theta =\pi \text{ or 3}\theta \text{=}\frac{\pi }{3}\\ \theta =\frac{\pi }{4}\text{ or }\theta =\frac{\pi }{9}\end{array}$