Answer
$\theta=\frac{\pi}{2}(2k+1)$, where $k$ is an integer
Work Step by Step
Since $\sec(\theta)=\dfrac{1}{\cos\theta}$, then it is undefined when the denominator (which is $\cos{\theta}$) is $0$.
Recall that $\cos{\theta}=0$ if $\theta=\frac{\pi}{2}(2k+1)$, where $k$ is an integer.
Therefore, the function is undefined when $\theta=\frac{\pi}{2}(2k+1)$, where $k$ is an integer.
