Compute $\tan 180^\circ$.
To compute $\tan 180^\circ$, I need to recall the definition of the tangent function in terms of sine and cosine. I know that $\tan \theta = \frac{\sin \theta}{\cos \theta}$ for any angle $\theta$. So, I can plug in $\theta = 180^\circ$ and get $\tan 180^\circ = \frac{\sin 180^\circ}{\cos 180^\circ}$. Now, I need to remember the values of sine and cosine for 180 degrees. I can use the unit circle as a reference, and see that 180 degrees corresponds to the point $(-1, 0)$ on the circle. That means that $\cos 180^\circ = -1$ and $\sin 180^\circ = 0$. So, I can simplify the fraction and get $\tan 180^\circ = \frac{0}{-1} = 0$. 