Evaluate $\sin(1998^\circ+237^\circ)\sin(1998^\circ-1653^\circ)$.
We have that
\begin{align*}
\sin (1998^\circ + 237^\circ) \sin (1998^\circ - 1653^\circ) &= \sin 2235^\circ \sin 345^\circ \\
&= \sin 75^\circ \sin (-15^\circ) \\
&= -\sin 75^\circ \sin 15^\circ \\
&= -\cos 15^\circ \sin 15^\circ \\
&= -\frac{1}{2} (2 \cos 15^\circ \sin 15^\circ) \\
&= -\frac{1}{2} \sin 30^\circ \\
&= \boxed{-\frac{1}{4}}.
\end{align*}