The τ polarisation has been studied with the e+e- → τ+τ- data collected by the DELPHI detector at LEP in 1993, 1994 and 1995 around the Z resonance firstly through the exclusive decay channels evv̄, μvvμ, πv, ρv, and a1v and secondly with an inclusive hadronic analysis which benefits from a higher efficiency and a better systematic precision. The results have been combined with those previously published on 1990 to 1992 DELPHI data, to produce results which reflect the full LEP-1 statistics. The fit of the τ polarisation dependence on the production angle yielded the polarisation parameters Aτ = 0.1359 ± 0.0096 and Ae = 0.1382 ± 0.0116. From these results the ratio of the vector and axial-vector effective couplings v̄τ/āτ = 0.0683 ± 0.0048 and v̄e/āe = 0.0694 ± 0.0058 have been derived, compatible with e-τ universality. With the assumption of lepton universality, the ratio of vector to axial-vector effective couplings for leptons v̄ι/āι = 0.0687 ± 0.0037 was obtained, implying a value of the effective weak mixing angle sin2 θlepteff= 0.23282 ± 0.00092.