(a) $\sin 7\theta + \sin \theta – \sin 4\theta = 0$

$ \Rightarrow $ $2\sin 4\theta \cos 3\theta – \sin 4\theta = 0$

$ \Rightarrow $ $\sin 4\theta (2\cos 3\theta – 1) = 0 $

$\Rightarrow \sin 4\theta = 0,\,{\rm{ }}\cos 3\theta = \frac{1}{2}$

Now $\sin 4 \theta = 0$ $ \Rightarrow $ $4\theta = \pi $ $ \Rightarrow $ $\theta = \frac{\pi }{4}$.

and $\cos 3\theta = \frac{1}{2}$ $ \Rightarrow $ $3\theta = \frac{\pi }{3}$ $ \Rightarrow $ $\theta = \frac{\pi }{9}$.