Explanation

(a)
$\sin{6\theta + \sin{4\theta + \sin{2\theta = 0}}}$
$\Rightarrow \sin{6\theta + \sin{2\theta + \sin{4\theta = 0}}}$
$\Rightarrow 2\sin{4\ \theta\cos{2\theta + \sin{4\theta = 0}}}$
$\Rightarrow \ \sin{4\theta(2\cos{2\theta + 1) = 0}}$
$\Rightarrow \ 2\cos{2\theta = - 1\ \Rightarrow \cos{2\theta = - \frac{1}{2}}}$
$\Rightarrow \ \cos{2\theta = \cos\frac{2\pi}{3}}$
$\Rightarrow 2\theta = 2n\pi \pm \frac{2\pi}{3}\ \Rightarrow \ \theta = n\pi \pm \frac{\pi}{3}$
and $\sin{4\theta = 0\ \Rightarrow 4\theta =}n\pi\ \Rightarrow \ \theta = \frac{n\pi}{4}$
$\Rightarrow \ \theta = \frac{n\pi}{4}\ or\ \ n\pi \pm \frac{\pi}{3}$