Using the data collected with the L3 detector at LEP between 1990 and
1995, corresponding to an integrated luminosity of 149 pb(-1), the tau
longitudinal polarisation has been measured as a function of the prod
uction polar angle using the tau decays tau(-) --> h(-)nu(tau) (h = pi
,rho,a(1)) and tau(-)-->l(-)<(nu)over bar>(l)nu(tau) (l = e,mu). From
this measurement the quantities A(c) and A(tau), which depend on the c
ouplings of the electron and the tau to the Z, are determined to be A(
c) = 0.1678 +/- 0.0127 +/- 0.0030 and A(tau) = 0.1476 +/- 0.0088 +/- 0
.0062, consistent with the hypothesis of e-tau universality, Under thi
s assumption a value of A(l) = 0.1540 +/- 0.0074 +/- 0.0044 is obtaine
d, yielding the value of the effective weak mixing angle sin(2)<(theta
)over bar>(W) = 0.2306 +/- 0.0011. (C) 1998 Elsevier Science B.V. All
rights reserved.