  We analyze the impact of the CP-violating observables in the $B_d\to
\rho^{\pm} \pi^{\mp}$ system, combined with the precise measurement of
$\sin2\beta$, in the extraction of the CKM matrix. We explore two strategies
for determining the Unitarity Triangle in these modes. Computing the penguin
parameters $(r_{\pm}, \phi_{\pm})$ and the ratio of two trees $(r_{t},
\phi_{t})$ within QCD factorization yields a precise determination of
$(\bar\rho, \bar\eta)$, reflected by a weak dependence on $\phi_{\pm}$, which
is shown to be a second order effect, as in the $B_d \to \pi^+ \pi^-$ system.
Moreover, we find that the dependence on penguin amplitudes $r_{\pm}$ in
$B_d\to \rho^{\pm} \pi^{\mp}$ is less pronounced than in the $B_d \to \pi^+
\pi^-$ case, since penguin contributions $r_{\pm}\approx r_{\pi\pi}/3$,
implying an important simplification in our analysis. Independent experimental
tests of the factorization framework are proposed and discussed, using $B_d \to
\pi^+ \pi^-$ and $B_d \to \rho^{\pm} \rho^{\mp}$ modes.
