Show that if $x \neq 0,\pm 2 \pi,\pm 4 \pi, \dots$, then
$\frac{1}{\tan(x/2)}=2 \sum_{j=1}^{\infty}\sin(jx)$
in Cesàro way/sense. Some hint whether to manipulate
$\sum_{j=1}^{\infty}a_j(x)=\sum_{j=1}^{\infty}\sin(jx) \tag1$
into (using partial sum of ($1$)) $\frac{1}{n}\sum_{j=1}^{n}\sin(jx)= \dots$