Explanation

(b)
As $\sin{\theta = \frac{1}{2}}$ and $\cos{\phi = \frac{1}{3}}$
$\Rightarrow \theta = \frac{\pi}{6}$ and $0 < \left( \cos{\phi = \frac{1}{3}} \right) < \frac{1}{2}\$
$\left\lbrack as,\ 0 < \frac{1}{3} < \frac{1}{2} \right\rbrack$
$\Rightarrow \ \ \theta = \frac{\pi}{6}$ and $\cos^{- 1}{(0) >}\phi > \cos^{- 1}\left( \frac{1}{2} \right)$
$\left\lbrack the\ sign\ changed\ as\cos{x\ is\ decreasing\ between\ \left( 0,\frac{\pi}{2} \right)} \right\rbrack$
$\Rightarrow \theta = \frac{\pi}{6}\ \ and\frac{\pi}{3} < \phi < \frac{\pi}{2}$
$\Rightarrow \frac{\pi}{2} < \theta + \phi < \frac{2\pi}{3}$
$\therefore\ \ \phi + \theta \in \left( \frac{\pi}{2},\frac{2\pi}{3} \right)$