Prove that if $x$ is a non-zero rational number, then $\tan(x)$ is not a rational number and use this to prove that $\pi$ is not a rational number.

Question

Prove that if $x$ is a non-zero rational number, then $\tan(x)$ is not a rational number and use this to prove that $\pi$ is not a rational number.

I heard that this was proved two hundred years ago. I need this proof because I want to know the proof of why $\pi$ is not rational.

I need the simplest proof!

thanx !