# How do you evaluate arc cot(cot(-pi/4)) without a calculator?

If we rewrite the original problem as $\arctan \left(\frac{1}{\tan} \left(- \frac{\pi}{4}\right)\right)$
$\arctan \left(\frac{1}{\tan} \left(- \frac{\pi}{4}\right)\right) = \arctan \left(\frac{1}{-} 1\right) = \arctan \left(- 1\right) = - \frac{\pi}{4}$