Prove Theorem 2: Let $n \geq 1$ be an integer and $A(z) = \sum_{k=0}^{n-1} a_k z^k$ a nonzero polynomial such that $a_k \in \{-1, 0, 1\}$ for all $0 \leq k \leq n-1$. Then for all integer $L \geq 1$ we have
$$\sup_{\theta \in \left[-\frac{\pi}{L}, \frac{\pi}{L}\right]} \left|A\left(e^{i\theta}\right)\right| \geq \frac{1}{n^{L-1}}$$