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Using data taken with the CLEO II detector at the Cornell Electron Storage Ring, we present the first full angular analysis in the color-suppressed modes B0→J/ψK*0 and B+→J/ψK*+. This leads to a complete determination of the decay amplitudes of these modes including the longitudinal polarization γL/γ=0.52±0.07±0.04 and the P wave …