Answer
$\theta=k\pi$, where $ k$ is an integer.
Work Step by Step
Since $\cot(\theta)=\dfrac{\cos\theta}{\sin\theta}$, then it is undefined when the denominator (which is $\sin{\theta}$) is $0$.
Recall that $\sin\theta=0$ if $\theta= k\pi$, where $k$ is an integer, therefore the function is defined on all real numbers except $\theta=k\pi$, where $ k$ is an integer.
