Answer
Rolle's theorem does not apply because $f(x)$ is discontinuous.
Work Step by Step
Look at the function and its endpoints.
$f(x)=cot\frac{\pi}{2}$ over $[\pi,3\pi]$
$f(\pi)=f(3\pi)=0$
But since there's a vertical asymptote at $f(2\pi)$, Rolle's theorem does not apply because $f(x)$ is discontinuous, where continuity is a pre-requisite for Rolle's Theorem.