We describe a new method for extracting weak, CP-violating phase informatio
n, with no hadronic uncertainties, from an angular analysis of B --> V1V2 d
ecays, where V-1 and V-2 are vector mesons. The quantity sin(2)(2 beta + ga
mma) can be cleanly obtained from the study of decays such as B-d(0)(t) -->
D*(+/-)rho(+/-), D*(+/-)a(1)(+/-), D(-)*K-0((-))*(0), etc. Similarly, one
can use B-s(0)(t) --> D*K-+/-(s)*(+/-) to extract sin(2)gamma. There are no
penguin contributions to these decays. It is possible that sin(2)(2 beta gamma) will be the second function of CP phases, after sin2 beta, to be me
asured at B factories.