The complex number $z$ is such that $|z|=1,\:z\neq1\:and\:w=\large|\frac{z-1}{z+1}|.$ Then the real part of $w$ is ?

Question

$\begin{array}{1 1}(A) \;\large\frac{1}{|z+1|}^2 \\(B)\; \large\frac{-1}{|z+1|}^2 \\(C)\;\large\frac{\sqrt 2}{|z+1|}^2\\(D)\;0\end{array}$