Answer
$2.47, 5.61$.
Work Step by Step
This equation is the same as: $cot(\theta)=-\frac{5}{4}.$
The domain of $\tan^{-1}{x}$ is the range of $\tan{x}$, which is the real numbers.
The range of $\tan^{-1}{x}$ is a specified domain of $\tan{x}$, i.e. $\left(− \frac{\pi}{2} , \frac{\pi}{2} \right)$.
We know that $\cot^{-1}(x)=\tan^{-1}{\frac{1}{x}}$.
After using a calculator in radian mode the solutions for $\cot^{-1}{-\frac{5}{4}}=\tan^{-1}{-\frac{4}{5}}$ is $-0.67$ (given by the calculator) and because the cot function has a period of $\pi$ the first solution is: $-0.67+\pi\approx2.47$ and the second solution is: $-0.67+2\pi\approx5.61$.
