  We consider the possibility of measuring both $\sin (2 \beta)$ and $\cos (2
\beta)$ in the KM unitarity triangle using the process $B^0 \to
D^{*+}D^{*-}K_s$. This decay mode has a higher branching fraction (O(1%)) than
the mode $B^0 \to D^{*+}D^{*-}$. We use the factorization assumption and heavy
hadron chiral perturbation theory to estimate the branching fraction and
polarization. The time dependent rate for $B^0(t) \to D^{*+} D^{*-} K_s$ can be
used to measure $\sin (2 \beta)$ and $\cos(2 \beta)$ . Furthermore, examination
of the $D^{*+} K_s$ mass spectrum may be the best way to experimentally find
the broad $1^+$ p-wave $D_s$ meson.
