Explanation

(b)
Let $\theta = \cos^{- 1}\left( - \frac{1}{2} \right)$
$\Rightarrow \ \cos{\theta = - \frac{1}{2} = - \cos\left( \frac{\pi}{3} \right)}$
$= \cos{\left( \pi - \frac{\pi}{3} \right) = \cos\left( \frac{2\pi}{3} \right)}$
$\Rightarrow \ \theta = 2n\pi \pm \frac{2\pi}{3}$
$\Rightarrow \ \ \theta = \frac{4\pi}{3},\ \frac{8\pi}{3},\ \frac{10\pi}{3},\ \frac{14\pi}{3},\ \ldots$