Answer
the period is $\frac{\pi}{2}$
Work Step by Step
To find the period, one must first find $b$ in the base equation of tangent functions $f(x)=a\cdot $tan$(b(x-c))+d$, then use $\frac{\pi}{b}$. In this case, $b$ is $2$, so the period is $\frac{\pi}{2}$
