Answer
$\frac{\pi}{3},\frac{2\pi}{3},\frac{4\pi}{3},\frac{5\pi}{3}$
Work Step by Step
Step 1. $sec^2(\theta)=4 \longrightarrow sec\theta=\pm2 \longrightarrow cos\theta=\pm\frac{1}{2}$
Step 2. For $cos\theta=\frac{1}{2}$, we have $\theta=2k\pi+\frac{\pi}{3}$ and $\theta=2k\pi+\frac{5\pi}{3}$
Step 3. For $cos\theta=-\frac{1}{2}$, we have $\theta=2k\pi+\frac{2\pi}{3}$ and $\theta=2k\pi+\frac{4\pi}{3}$
Step 4. Within $[0,2\pi)$, we have $\theta=\frac{\pi}{3},\frac{2\pi}{3},\frac{4\pi}{3},\frac{5\pi}{3}$