Answer
See below
Work Step by Step
We know that the trigonometric function $\cos^{-1} (\frac{-1}{2})$ has the domain $[-1,1]$ and the range is: $[-\dfrac{\pi}{2}, \dfrac{\pi}{2}]$.
So, $\theta = \cos^{-1} (\dfrac{-1}{2})$
This implies that: $\theta=\dfrac{2\pi}{3}$ or, $120^{\circ}$
