Extraction of a Weak Phase from $B \to D^{(*)} \pi$

To observe CP-violating asymmetries through the interference of a weaker amplitude with a stronger one in $\bo \to D^{(*)} \pi$ and $\ob \to D^{(*)} \pi$ decays, one must collect enough events that the intensity associated with the weaker amplitude would be statistically significant. We show that provided the weaker amplitude is measured separately in $B^\pm \to D^{(*)\pm} \pi^0$ decays, the time-integrated approach requires around $2.5 \cdot 10^8 \ B \bar B$ pairs for measurements of the weak phase $\sin(2\beta + \gamma)$ with an uncertainty of $0.05$ or better. We also determine the optimal conditions for precise $2\beta + \gamma$ measurements and discuss the possibilities for resolving a discrete ambiguity.