How do you find cot^-1 (-1/sqrt3) without using a calculator?

Let the given expression be equal to y, so that cot y= $- \frac{1}{\sqrt{3}}$.
$\frac{1}{\sqrt{3}}$ is the value of cot for 30 degrees, as can be seen from the unit circle.
Since cot would be negative in IInd and IVth quadrant, coty would be $- \frac{1}{\sqrt{3}}$ for y= 180-30= 150 and y= 360-30= 330 degrees