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This paper reports an updated measurement of the standard model CP violation parameter sin 2β using the CDF Detector at Fermilab. The entire run I data sample of 110 pb-1 of proton-antiproton collisions at √s =1.8 TeV is used to identify a signal sample of ≈400 B→J/ ψKs0 events, where J/ψ→ μ+μ- and Ks0→ π+ π-. The flavor of the neutral B meson is identified at the time of production by combining information from three tagging algorithms: a same-side tag, a jet-charge tag, and a soft-lepton tag. A maximum likelihood fitting method is used to determine sin 2 β =0.79-0.44+0.41 (stat+syst). This value of sin 2 β is consistent with the standard model prediction, based upon existing measurements, of a large positive CP-violating asymmetry in this decay mode.