The polarization of tau leptons is measured using leptonic and hadronic tau lepton decays in Z -> tau(+)tau(-) events in proton-proton collisions at root s = 13 TeV recorded by CMS at the CERN LHC with an integrated luminosity of 36.3 fb(-1). The measured tau(-) lepton polarization at the Z boson mass pole is P-tau(Z) = -0.144 +/- 0.006 (stat) +/- 0.014 (syst) = -0.144 +/- 0.015, in good agreement with the measurement of the tau lepton asymmetry parameter of A(tau) = 0.1439 +/- 0.0043 = -P-tau(Z) at LEP. The tau lepton polarization depends on the ratio of the vector to axial-vector couplings of the tau leptons in the neutral current expression, and thus on the effective weak mixing angle sin(2)theta(eff)(W), independently of the Z boson production mechanism. The obtained value sin(2)theta(eff)(W) = 0.2319 +/- 0.0008(stat) +/- 0.0018(syst) = 0.2319 +/- 0.0019 is in good agreement with measurements at e(+)e(-) colliders.