# How do you evaluate csc (arctan(-1 / sqrt3))?

$- 2$
Let $a = a r c \tan \left(- \frac{1}{\sqrt{3}}\right) \in {Q}_{4}$, wherein sine is negative.
Then, $\tan a = - \frac{1}{\sqrt{3}} \mathmr{and} \sin a = - \frac{1}{2}$.
The given expression is $\csc a = \frac{1}{\sin} a = - 2$..