### Instruction: Compute $\tan 300^\circ$.### Response: I know that the tangent function is periodic with period $180^\circ$, so $\tan 300^\circ = \tan (300^\circ - 180^\circ) = \tan 120^\circ$.
To find $\tan 120^\circ$, I can use the reference angle of $60^\circ$ and the fact that tangent is odd, so $\tan 120^\circ = -\tan 60^\circ$.
I recall that $\tan 60^\circ$ is one of the special angles that can be derived from an equilateral triangle, and it is equal to $\sqrt{3}$.
Therefore, $\tan 300^\circ = -\sqrt{3}$.