What is the fundamental period of the function defined by ##f(x)= 3 - 2 cos^2 (pix/3)##?

3

##cos(x)## has a period of ##2pi## ##cos^2(x)## has a period of ##pi## the only periodic element of this function is the ##cos^2(pi x/3)## which repeats when the part inside the cosine reaches ##pi## Solving for ##pi x/3=pi## gives ##x=3## which is the fundamental period of this function