Elemental Number Theory: Proving that $\pi$ is irrational, assuming the following result: if $x$ is rational, $tan(x)$ is not.

Question

Question: Prove that $\pi$ is irrational, assuming the following result: if $x$ is rational, $tan(x)$ is not.

Proof: Let $x$ $\in$ $\mathbb Q$

I have seen Lambert's proof, however I am severely confused on where to begin. Do I now suppose $tan(x)$ is rational, then proceed by contradiction? Hints would be delightful!

Answer 1

Hint: Suppose $\pi/4$ is rational.

Answer 2

$$\tan (\pi)=0\in \mathbb Q $$

$$\implies \pi \notin \mathbb Q $$