With a data sample of 86 000 Z → τ+τ−(γ) events collected in 1990 through 1993 we have measured the polarization of τ-leptons as a function of the production polar angle using the following 1-prong τ decay modes: r- ~ e-~evT, r- --+/.t-Vuv~, r- ---+ 7r-(K-)v~, r- ~ p-v, and r- ---+ a~'v, We obtain for the ratio of vector to axial-vector weak neutral couplings for electrons gVe/gAe=0.0791±0.0099(stat)±0.0025 (syst) and taus gVτ/gAτ=0.0752±0.0063 (stat)±0.0045 (syst) consistent with the hypothesis of e - τ universality. Assuming universality of the e - τ neutral current we determine the effective electroweak mixing angle to be sin2 θeffw = 0.2309 ± 0.0016..