\[\sin x+\tfrac{1}{3}\sin\left(3x\right)+\tfrac{1}{5}\sin\left(5x\right)+\dots=%
\begin{cases}\frac{1}{4}\pi,&0<x<\pi,\\
0,&x=0,\\
-\frac{1}{4}\pi,&-\pi<x<0.\end{cases}\]