Pigeon Hole Principle in Unit Disk

Question

Let $n$ be a natural number such that $n \ge 2$ and given complex number $z_1, z_2, \ldots, z_n$ that is contained in an open unit disk centered at origin. Prove that there exists $\epsilon_l = \pm 1$ with $l = 1, 2, \ldots, n$ such that \begin{align*} \left|\sum_{l=1}^n \epsilon_l z_l\right|\le\sqrt{3} \end{align*}