$f: \mathbb{D} \to \mathbb{D}$ holomorphic, $f(\frac{1}{2}) + f(-\frac{1}{2}) = 0$. Prove $|f(0)| \leq \frac{1}{4}$
If $f \in \operatorname{Hol}(D)$, $f(\frac{1}{2}) + f(-\frac{1}{2}) = 0$, prove that $|f(0)| \leq \frac{1}{4}$