Find all functions f which are meromorphic in a neighborhood of $\left\{|z|\le 1 \right\}$ and such that $|f(z)|=1$ for $|z|=1$ , f has a double pole at $z=\frac{1}{2}$, a triple zero at $z=-\frac{1}{3}$ and no other zeros or poles in $\left\{|z|<1 \right\}$
I have no idea how can I do this problem :S! Maybe using laurent expansion and uniqueness of that , but I don't know how can I find the general form of such functions, please help me :/ I want to see an example.