How do you calculate the arctan(-1)?

arctan(−1)=(npi-pi/4), where $n$ is an integer i.e. arctan(−1) can take values such as $\left\{\ldots \ldots . , - 9 \frac{\pi}{4} , - 5 \frac{\pi}{4} , - \frac{\pi}{4} , 3 \frac{\pi}{4} , 7 \frac{\pi}{4} , \ldots . .\right\}$
arctan(−1) is the angle whose tangent is $- 1$.
As $\tan \left(- \frac{\pi}{4}\right) = - \tan \left(\frac{\pi}{4}\right) = - 1$ and tangent of angle has a cycle of $p$ radians
We can generally put arctan(−1)=(npi-pi/4), where $n$ is an integer i.e. arctan(−1) can take values such as $\left\{\ldots \ldots . , - 9 \frac{\pi}{4} , - 5 \frac{\pi}{4} , - \frac{\pi}{4} , 3 \frac{\pi}{4} , 7 \frac{\pi}{4} , \ldots . .\right\}$