Answer
$\theta=-\frac{\pi}{3}+2k\pi$ and $\theta=\frac{\pi}{3}+2k\pi$
Six example solutions for $k=0,\pm1$:
$-\frac{7\pi}{3}, -\frac{5\pi}{3}-\frac{\pi}{3}, \frac{\pi}{3}, \frac{5\pi}{3}, \frac{7\pi}{3} $
Work Step by Step
Given $cos\theta=\frac{1}{2}$,
we can find two $\theta$ values in $[-\pi, \pi]$ as $\theta=-\frac{\pi}{3}, \frac{\pi}{3},$
and the general solutions are $\theta=-\frac{\pi}{3}+2k\pi$ and $\theta=\frac{\pi}{3}+2k\pi$
where $k$ is any integer. Six example solutions for $k=0,\pm1$:
$-\frac{7\pi}{3}, -\frac{5\pi}{3}-\frac{\pi}{3}, \frac{\pi}{3}, \frac{5\pi}{3}, \frac{7\pi}{3} $
