Answer
$g(\theta)$ has vertical asymptotes at the values $\theta$ such that $\theta=\dfrac{\pi +2\pi k}{2}$ where $k$ is an integer.
Work Step by Step
$g(\theta)=\dfrac{\tan{\theta}}{\theta}=\dfrac{\sin{\theta}}{\theta\cos{\theta}}.$
Vertical asymptotes occur when the denominator alone is $0\to$
$\theta\cos{\theta}=0\to \cos{\theta}=0$ or $\theta=0.$
$\theta=0$ is rejected since $\sin{0}$ is also $0.$
$\cos{\theta}=0\to\theta=\pi k +\dfrac{\pi}{2}$ where $k$ is an integer.
