  Determination of the CP-violating parameters \sin 2\beta and \sin 2\beta' is
shown to be possible from B^0_d vs \bar{B}^0_d \to D^{*+}D^{*-} and B^0_s vs
\bar{B}^0_s \to D^{*+}_sD^{*-}_s decays {\it without} doing the angular
analysis. The P-wave dilution factors of these two asymmetries are found to be
0.89 and 0.90, respectively, using the factorization approximation and heavy
quark symmetry. The penguin-induced corrections amount to about 2% and 3% in
the corresponding B_d and B_s channels. Final-state rescattering effects could
be handled by detecting the neutral modes B^0_d and \bar{B}^0_d \to
D^{*0}\bar{D}^{*0}.
