I need to find an optimal $\theta$ that minimizes
$$\left\| \frac{c\:e^{j\theta}- a^H x}{\|a\|_2^2}a \right\|_2^2 \ ,$$ where $(\cdot)^H$ denotes complex conjugate transpose, $c \in \mathbb{R}$, $a, x \in \mathbb{C}^n$.
I am told that the optimal $\theta$ is angle of $a^H x$ such that $e^{j\theta}= \frac{a^H x}{|a^H x|}$, but I don't how to prove it. Can anyone prove this?