Answer
$\frac{\pi}{4}+k\pi$, $\frac{3\pi}{4}+k\pi$
Work Step by Step
$\sec^2\theta-2=0$
$\sec^2\theta=2$
$\sec\theta=\pm\sqrt{2}$
$\cos\theta=\pm\frac{1}{\sqrt{2}}$
$\cos\theta=\pm\frac{\sqrt{2}}{2}$
If $\cos \theta=\frac{\sqrt{2}}{2}$, then $\theta=\frac{\pi}{4}+2k\pi$ or $\theta=\frac{7\pi}{4}+2k\pi$.
If $\cos \theta=-\frac{\sqrt{2}}{2}$, then $\theta=\frac{3\pi}{4}+2k\pi$ or $\theta=\frac{5\pi}{4}+2k\pi$.
Combining these two cases, we get $\theta=\frac{\pi}{4}+k\pi$ and $\theta=\frac{3\pi}{4}+k\pi$.
