Answer
$1$
Work Step by Step
We know that $\tan{\theta}$ has a period of $180^{\circ}$ (thus $\tan{(\theta+k\cdot 180^0)}=\tan{\theta}$, where $k$ is an integer). Hence, first we try and find a value where the argument is between $0^{\circ}$ and $180^{\circ}$.
Note that
$\tan(405^{\circ})=\tan(405^{\circ}+(-2)\cdot180^{\circ})=\tan(45^{\circ})=1$
