Claim: there exists holomorphic function $g:\mathbb{C}\rightarrow\mathbb{C}$ such that: $\sin\left(z\right)=g\left(z\left(\pi-z\right)\right)$.
I had this idea than in a small enough neighborhood the function $z\left(\pi-z\right)$ is invertible with an holomorphic inverse, call it $h$, then in that small neighborhood $g\left(z\right)=\sin\left(h\left(z\right)\right)$. but I don't know how to extend it to $\mathbb{C}$. Any ideas about fixing this idea, or a new approach altogether?
