Answer
$ 30^{\circ}$ and $330^{\circ}$.
Work Step by Step
The value of $\cos \theta$ is positive, so $\theta$ may lie in either quadrant I or IV.
We know that $\cos 30^{\circ}=\frac{\sqrt 3}{2}$.
$30^{\circ}$ is in the first quadrant.
We can find the value of $\theta$ in the fourth quadrant using the identity
$\cos x=\cos (360^{\circ}-x)$
$\implies \cos 30^{\circ}= \cos(360^{\circ}-30^{\circ})=\cos 330^{\circ}$
The values of $\theta$ are $ 30^{\circ}$ and $330^{\circ}$.
