Why tan(pie)x + tanx is non periodic....???? plz explain me!!

period of tan((pie)x) is 1 and that of tanx is π, the sum of two periodic functions is periodic, if an integral multiple of the period of the first function is equal to (either the same or different) integral multiple of the period of the second function.

so m*1=n*π,m/n=pi which is impossible. That is why it is non-periodic.