Answer
$2.3154725$ radian
Work Step by Step
Ensuring that the calculator is in radian mode, we enter $\cot^{-1} (-0.92170128)$ as $\tan^{-1} (\frac{1}{-0.92170128})$ into the calculator and solve:
$\tan^{-1} (\frac{1}{-0.92170128})\approx-0.82612012$ radian
Adding the solution to $\pi$ radian:
$\pi+(-0.82612012)=2.3154725$ radian