Answer
$tan(\theta) = tan(\theta+n\cdot 360^{\circ})$
Work Step by Step
One full rotation is equal to $360^{\circ}$. Therefore, $\theta$ and $\theta+n\cdot 360^{\circ}$ are co-terminal angles for any integer $n$. That is, they point in precisely the same direction.
Since the angles point in the same direction, the x- and y-coordinates are the same.
$tan(\theta) = \frac{y}{x}$
$tan(\theta+n\cdot 360^{\circ}) = \frac{y}{x}$
Since the x- and y-coordinates are the same, $tan(\theta) = tan(\theta+n\cdot 360^{\circ})$
