Answer
$1$
Work Step by Step
When $P$ is the period of $f(x)$ then we have
$ f(x+p)=f(x)$
Here, we have $ \theta= (-\dfrac{3 \pi}{4})$ lies in the third quadrant; thus, we will have to add $2 \pi$ in order to get the co-terminal angle.
But $\theta'=\dfrac{-3 \pi}{4}+ 2\pi=\dfrac{5 \pi}{4}$
and $\theta''=\dfrac{5 \pi}{4}-\pi=\dfrac{\pi}{4}$
Thus, we have $\tan(\dfrac{5 \pi}{4})=\tan \dfrac{\pi}{4}$
Hence, $\tan \dfrac{\pi}{4}=1$
