  The extraction of CKM-matrix-element information from hadronic B-decays
generally suffers from discrete ambiguities, hampering the diagnosis of physics
beyond the Standard Model. We show that a measurement of the rate asymmetry,
which is CP-violating, in
$B^{\pm}\to\rho^{\pm}\rho^0(\omega)\to\rho^{\pm}\pi^+\pi^-$, where the
invariant mass of the $\pi^+\pi^-$ pair is in the vicinity of the $\omega$
resonance, can remove the mod($\pi$) uncertainty in $\alpha\equiv arg [-V_{td}
V_{tb}^\ast/(V_{ud}V_{ub}^\ast)]$ present in standard analyses.
