Answer
$-\dfrac{\pi}{4}$
Work Step by Step
We know that the trigonometric function $\tan^{-1} (1)$ has domain R and the range is: $[-\dfrac{\pi}{2}, \dfrac{\pi}{2}]$.
So, $\theta = \tan^{-1} (-1) $
This implies that: $\theta=-\dfrac{\pi}{4}$
