### Instruction: Compute $\tan 300^\circ$.### Response: I recall that the tangent function is defined as the ratio of the sine and cosine functions, so $\tan \theta = \frac{\sin \theta}{\cos \theta}$.
I also remember that the trigonometric functions have a periodicity of $360^\circ$, so adding or subtracting multiples of $360^\circ$ does not change their values.
Therefore, $\tan 300^\circ = \tan (300^\circ - 360^\circ) = \tan (-60^\circ)$.
I can use the reference angle of $60^\circ$ to find the value of $\tan (-60^\circ)$.
I know that $\tan 60^\circ = \sqrt{3}$, so $\tan (-60^\circ) = -\tan 60^\circ = -\sqrt{3}$.
Alternatively, I can use the symmetry of the tangent function to find the value of $\tan (-60^\circ)$.
I know that $\tan$ is an odd function, meaning that $\tan (-\theta) = -\tan \theta$.
Therefore, $\tan (-60^\circ) = -\tan 60^\circ = -\sqrt{3}$.