Answer
$\theta = 45^{\circ}$ or $315^{\circ}$
Work Step by Step
1. Since $cos\theta$ is positive, $\theta$ must be in quadrant I or IV.
2. The reference angles is $45^{\circ}$.
The other angle in IV quadrant must be :
$360^{\circ}-45^{\circ}=315^{\circ}$
