Example based on maximum principle for heat equation

Question

Let $R =\{ (x,t)~|~ 0 < x < \pi,~0\le t \le T \} $ and $u$ solves the heat equation with $$u(0,t)=u(\pi,t)=0,~0 \le t \le T $$ $$ u(x,0) =\sin^{2}(x),~0\le x \le \pi. $$ Then how by using maximum principle we can show that $0 \le u(x,t) \le e^{-t} \sin{x}~$ in $R$.