Consider the rotation $R_\alpha(z) = \alpha z, R_\alpha : S^1 \to S^1$. Show that
$R_\alpha$is ergodic with respect to Haar measure on $S^1$ $\iff$ $\alpha$ is not a root of unity.
I don't know how to show the $\Leftarrow$ implication. Can someone please help me? I know I have to consider some Fourier series, but I fail to solve this exercise.