$\displaystyle f(z)=log(\frac{1+z}{1-z}) $ defined by branch cuts on the real axis from negative infinity to -1 and from 1 to infinity, f(0)=0

show by setting $\displaystyle z=e^{i\theta} $ that f maps the disc |z|<1 onto the infinite strip $\displaystyle \{ x+iy : -\frac{\pi}{2}<y<\frac{\pi}{2} \} $