Density in the unit circle

Here's an interesting Complex Analysis question. It's probably not too difficult, but I'm just not seeing the solution for some reason:

Show that $\displaystyle \{ e^{ki}|k\in \mathbb{Z},k\geq 0\}$ is dense in the unit circle.

So I think this reduces to the following question:

Given $\displaystyle \epsilon >0$ and $\displaystyle \theta \in \mathbb{R}$, show that there are integers $\displaystyle n$ and $\displaystyle k$ with $\displaystyle k\geq 0$ such that

$\displaystyle |e^{i(\theta - k+2n\pi)}-1|<\epsilon$.

A hint how to proceed would be nice.