1. We start with the first question: Calculate $\tan 180^\circ$. 2. Recall the definition of tangent in terms of sine and cosine: $$\tan \theta = \frac{\sin \theta}{\cos \theta}$$ 3. Evaluate sine and cosine at $180^\circ$: $$\sin 180^\circ = 0$$ $$\cos 180^\circ = -1$$ 4. Substitute these values into the tangent formula: $$\tan 180^\circ = \frac{0}{-1} = 0$$ 5. Therefore, the answer is: $$\boxed{0}$$ This completes the solution for the first question.