The polarization of [tau] leptons produced in the reaction e[superscript]+e[superscript]-→[tau][superscript]+[tau][superscript]- near the peak of the Z° resonance has been measured using a sample of 24904 [tau][superscript]+[tau][superscript]- events, with an estimated background of 1.5%. We have selected 4562 [tau]→ e[nu][macron][nu], 2218 [tau]→[pi][nu] and 5133 [tau]→[rho][nu] candidates. The mean value obtained is P[subscript][tau]=-0.176± 0.029. This corresponds to a ratio of the neutral current vector to the axial-vector coupling constants of the [tau] lepton of g[subscript]spV[tau]/g[subscript]spA[tau]=0.088± 0.014. This leads to a value of the electroweak mixing angle of sin[superscript]2[theta][subscript]W=0.2280± 0.0036. This result is in good agreement with previous measurements of the weak mixing angle from the study of the Z° lineshape and the forward-backward asymmetries in the processes Z°→ l[superscript]+l[superscript]- and Z°→ q[macron]q.