We suggest a novel method to determine the sign of cos(2 beta) in the decays B --> psi K, by creating interference between KL and KS final states via ``regeneration, that is propagation through a matter target region to convert some KL to KS. The determination of this quantity resolves an ambiguity between beta and (90o - beta) that remains after the standard measurements of sin(2 beta) and may turn out to be important in resolving whether the result is in agreement with Standard Model predictions or indicates the presence of new physics. We find the measurement is feasible at a B-factory, but requires several years of high-luminosity running with a regeneration target affecting a significant fraction of the detector.
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