Answer
$120^{\circ}$ and $240^{\circ}$
Work Step by Step
$\cos\theta=-\frac{1}{2}$
$\cos\theta$ is negative in the second and third quadrants.
$\cos 60^{\circ}=\frac{1}{2}$
Recall that $\cos(180^{\circ}-x)=\cos(180^{\circ}+x)=-\cos x$
$\implies -\cos 60^{\circ}=-\frac{1}{2}=\cos(180^{\circ}-60^{\circ})=\cos 120^{\circ}$
and
$-\frac{1}{2}=\cos(180^{\circ}+60^{\circ})=\cos 240^{\circ}$
Values of $\theta$ are $120^{\circ}$ and $240^{\circ}$
