Prove that a function $f: T^{2} \to T^{2}$ is topological transistive.

Question

The question I`m not getting is the following:

$\alpha$ is irrational and $f: T^{2} \to T^{2}$ is the homeomorphic function from to 2-torus unto itself given by $f(x,y)=(x+\alpha,x+y)$.

$a )$ Prove that every non-empty, open, $f$-invariant set is dense.

My attempt:

I know I have to show that every orbit of this function is dense, but I don`t know how. Could you please help me?

Yours,

Pim