Find a conformal map of the sector \{ |\text{arg} z| < \frac{\pi}{3} \} onto the open unit disk mapping 0 to -1 and \infty to +1. Sketch the images of radial lines and of arcs of circles centered at 0. Is the map unique?

The back of the book says that w=\frac{z^{\frac{3}{2}}-s}{z^{\frac{3}{2}}+s}, for any s>0 works. Though the map is not unique, the sketch is. I do not see how they got this map. Also, why isn't this map unique? I do not see why. Thank you.