Answer
FALSE
Work Step by Step
The statement would be true only if $–\frac{\pi}{2} \lt θ \lt \frac{\pi}{2}$.
However, for any $θ$ outside this interval, the inverse tangent function would just produce an angle in $(–\frac{\pi}{2} , \frac{\pi}{2}$) with the same tangent.
Thus, in these cases, the statement is false.
For example, the point (–1, –1) can be represented by ($\sqrt {2}, \frac{5\pi}{4}$), in polar coordinates. But $tan^{–1} (\frac{–1}{–1}) = \frac{\pi}{4} \ne \frac{5\pi}{4}$.
