computation of a double serie

Hello, I have a problem to compute the following serie :

$S(t,\delta)=\sum_{\substack {k, l\geq 0 \\ k-l > 0 }} {(1-t)^{k+l}\cdot\frac{\sin\big((k-l)\delta\big)}{k-l}\cdot\frac{kl}{k+l}}= ?
$

More precisly, my aim is to know if $t^2 S(t,\delta)\stackrel{t\rightarrow0}{\rightarrow}0$ .

Thanks for this lecture.