I know this question has been asked before... I went through all of the questions of this sort and none of them had an answer using Cauchy's criterion.

I know that $\sin(n)$ does not converge and I know how to show it in different ways (sub-sequences and unity of the limit), but I'm stuck with Cauchy... I can't figure it out.

I have to show that:
$\exists \epsilon>0$ such that $\forall N\in\mathbb N, \exists m,n > N$ such that $|\sin(m)−\sin(n)|>\epsilon$.

How do I find $\epsilon$ and $m,n$ that will do it?