Using the data collected with the L3 detector at LEP between 1990 and 1995, corresponding to an integrated luminosity of 149 pb−1, the τ longitudinal polarisation has been measured as a function of the production polar angle using the τ decays τ−→h−ντ (h=π,ρ,a1) and <math><mtext>τ</mtext><msup><mi></mi><mn>−</mn></msup><mtext>→ℓ</mtext><msup><mi></mi><mn>−</mn></msup><mtext>ν</mtext><mtext>̄</mtext><msub><mi></mi><mn>ℓ</mn></msub><mtext>ν</mtext><msub><mi></mi><mn>τ</mn></msub></math> (ℓ=e,μ). From this measurement the quantities Ae and Aτ, which depend on the couplings of the electron and the τ to the Z, are determined to be Ae=0.1678±0.0127±0.0030 and Aτ=01540±0.0088±0.0062, consistent with the hypothesis of e–τ universality. Under this assumption a value of <math><mtext>A</mtext><msub><mi></mi><mn>ℓ</mn></msub><mtext>=0.1540±0.0074±0.0044</mtext></math> is obtained, yielding the value of the effective weak mixing angle <math><mtext>sin</mtext><msup><mi></mi><mn>2</mn></msup><mtext>θ</mtext><msub><mi></mi><mn><mtext>W</mtext></mn></msub><mtext>=0.2306±0.0011</mtext></math>.Facultad de Ciencias Exactas