Answer
$2.47,5.61$
Work Step by Step
Use a calculator, $4cot\theta=-5 \Longrightarrow tan\theta=-\frac{4}{5} \Longrightarrow \theta=tan^{-1}(-\frac{4}{5})=\pi-tan^{-1}(\frac{4}{5})\approx2.47$ and $2\pi-tan^{-1}(\frac{4}{5})\approx5.61$ in $[0,2\pi)$.
