We know that sinus is 2pi-periodic.
sin(2x) -> find t such as sin(2(x+t))=sin(2x)
This means that 2t=2pi -> t=pi
Do the same for sin(x/2) and finding t' such as sin((x+t')/2)=sin(x/2)
The period of the function will be gcd(t,t')