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Time-dependence in $B^0(t) \to \pi^+ \pi^-$ and $\ob(t) \to \pi^+ \pi^-$ isutilized to obtain a maximal set of information on strong and weak phases. Onecan thereby check theoretical predictions of a small strong phase $\delta$between penguin and tree amplitudes. A discrete ambiguity between $\delta\simeq 0$ and $\delta \simeq \pi$ may be resolved by comparing the observedcharge-averaged branching ratio predicted for the tree amplitude alone, usingmeasurements of $B \to \pi l \nu$ and factorization, or by direct comparison ofparameters of the Cabibbo-Kobayashi-Maskawa (CKM) matrix with those determinedby other means. It is found that with 150 fb$^{-1}$ from BaBar and Belle, thisambiguity will be resolvable if no direct CP violation is found. In thepresence of direct CP violation, the discrete ambiguity between $\delta$ and$\pi - \delta$ becomes less important, vanishing altogether as $|\delta| \to\pi/2$. The role of measurements involving the lifetime difference betweenneutral $B$ eigenstates is mentioned briefly.Comment: 14 pages, LaTeX, 5 figures, to be published in Phys. Rev. D. Updated  version with one reference change

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

Strong and weak phases from time-dependent measurements of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mrow><mml:mover><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mo>→</mml:mo></mml:mrow></mml:mover></mml:mrow></mml:mrow><mml:mi>π</mml:mi><mml:mi>π</mml:mi></mml:math>

Strong and weak phases from time-dependent measurements ofB→ππ