Explanation

(c)
Given, $\sin{3\theta - \sin{\theta = 0}}$
$\Rightarrow \ 2\cos{\left( \frac{3\theta + \theta}{2} \right)\sin\left( \frac{3\theta - \theta}{2} \right) =}0$
$\Rightarrow \ \cos{2\theta.\sin{\theta = 0}}$
$\Rightarrow \ \cos{2\theta = 0}$ or $\sin{\theta = 0,\ \pi,\ 2\pi}$
$\Rightarrow \ \ 2\theta = \frac{\pi}{2},\ \frac{3\pi}{2},\ \frac{5\pi}{2},\ \frac{7\pi}{2}$ or $\theta = \pi$ ($\because\ \theta \in (0,\ 2\pi)$)
$\Rightarrow \ \theta = \frac{\pi}{4},\ \frac{3\pi}{4},\ \frac{5\pi}{4},\ \frac{7\pi}{4}$ or $\theta = \pi$
Hence, total number of solutions are 5