In Appendix B of QFT in a nutshell by Zee, a review of group theory is given. In the last paragraph of the appendix on page 533, he briefly discusses the helicity quantization of massless particles.
Firstly, he takes a rotation of $4\pi$ and considers possible helicities by using $exp(i4 \pi h) = 1$, where h is the helicity. Why he considers a rotation by $4\pi$ is not clear to me, and also why the path traced by this rotation can be shrunk to a point. Secondly, why is he not quantizing the helicity algebraically as conventionally done as in the case of angular momentum, but instead applying topological arguments. Is there a relation between the two?