How to prove that $|e^{i(c+l\cdot \omega)}-1|\geq \tilde{k}|l|^{-(m+\epsilon)}$ if $dist|c+l\cdot \omega, 2\pi\mathbb{Z}|\geq k|l|^{-(m+\epsilon)}$?

Question

Let $\epsilon>0$. I know that for almost every $c\in (0,2\pi)$ there is a constant $k>0$ such that $dist|c+l\cdot \omega, 2\pi\mathbb{Z}|\geq k|l|^{-(m+\epsilon)}$ for all $l \in \mathbb{Z}^m-\{0\}$. How can i prove that $|e^{i(c+l\cdot \omega)}-1|\geq \tilde{k}|l|^{-(m+\epsilon)}$?