The tau polarisation has been studied with the e(+)e(-) --> tau(+)tau(-) da
ta collected by the DELPHI detector at LEP in 1993, 1994 and 1995 around th
e Z resonance firstly through the exclusive decay channels ev (v) over bar,
mu v (v) over bar, pi v, rho v and a(1)v and secondly with an inclusive ha
dronic analysis which benefits from a higher efficiency and a better system
atic precision. The results have been combined with those previously publis
hed on 1990 to 1992 DELPHI data, to produce results which reflect the full
LEP-1 statistics. The fit of the tau polarisation dependence on the product
ion angle yielded the polarisation parameters A(tau) = 0.1359 +/- 0.0096 an
d A(epsilon) = 0.1382 +/- 0.0116. From these results the ratio of the vecto
r and axial-vector effective couplings (v) over bar/(a) over bar(tau) = 0.0
683 +/- 0.0048 and (v) over bar/(a) over bar(e) = 0.0694 +/- 0.0058 have be
en derived, compatible with e-tau universality. With the assumption of lept
on universality, the ratio of vector to axial-vector effective couplings fo
r leptons (v) over bar(l)/(a) over bar(l) = 0.0687 +/- 0.0037 was obtained,
implying a value of the effective weak mixing angle sin(2) theta(eff)(lept
) = 0.23282 +/- 0.00092.