The forward-backward asymmetry of bottom quarks is measured with statistics of approximately 80 000 hadronic Z0 decays produced in e+e- collisions at a centre of mass energy of square-root s almost-equal-to M(z). The tagging of b quark events has been performed using the semileptonic decay channel b --> X + mu. Because the asymmetry depends on the weak coupling, this leads to a precise measurement of the electroweak mixing angle sin2 theta(w). The experimental result is A(FB)b = 0.115 +/- 0.043(stat.) +/- 0.013(syst.). After correcting the value for the B0B0BAR mixing this becomes A(FB)b = 0.161 +/- 0.060(stat.) +/- 0.021 (syst.) corresponding to sin2 theta(w)MSBAR = 0.221 +/- 0.011 (stat.) +/- 0.004 (syst.).
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