Given an entire function $f(z)$ we know that $ \log f(z)=\log|f(z)|+i \arg f(z)$
Let $f(z)=\frac{z-a}{z-\bar a}$, for complex number $a$. How to show that $\arg f(z)=\tan^{-1}(???)$ on the real line $\mathbb R$. (I don't know what is exactly inside $\tan^{-1}$)