Explanation

(a)
Let $f(x) = 3\sin x - 4\sin^{3}x = \sin{3x}$
Since, $\sin x$ is increasing in the interval$\left\lbrack - \frac{\pi}{2},\frac{\pi}{2} \right\rbrack$
$\therefore\ \ - \frac{\pi}{2} \leq 3x \leq \frac{\pi}{2}\ \ \ \ \Rightarrow \ \ \ \ \ - \frac{\pi}{6} \leq x \leq \frac{\pi}{6}$
Thus, length of interval $= \left| \frac{\pi}{6}\left( - \frac{\pi}{6} \right) \right| = \frac{\pi}{3}$