The polarization ofτleptons is measured using leptonic and hadronicτlepton decays in Z →τ⁺τ⁻events in proton-proton collisions at$$ \sqrt{s} $$$\sqrt{s}$= 13 TeV recorded by CMS at the CERN LHC with an integrated luminosity of 36.3 fb⁻¹. The measuredτ⁻lepton polarization at the Z boson mass pole is$$ {\mathcal{P}}_{\tau}\left(\textrm{Z}\right) $$$P_{\tau }\left(Z\right)$= −0.144 ± 0.006 (stat) ± 0.014 (syst) = −0.144 ± 0.015, in good agreement with the measurement of theτlepton asymmetry parameter ofA_τ= 0.1439 ± 0.0043 =$$ -{\mathcal{P}}_{\tau}\left(\textrm{Z}\right) $$$-P_{\tau }\left(Z\right)$at LEP. Theτlepton polarization depends on the ratio of the vector to axial-vector couplings of theτleptons in the neutral current expression, and thus on the effective weak mixing angle sin²$$ {\theta}_{\textrm{W}}^{\textrm{eff}} $$${\theta }_W^{\mathrm{eff}}$, independently of the Z boson production mechanism. The obtained value sin²$$ {\theta}_{\textrm{W}}^{\textrm{eff}} $$${\theta }_W^{\mathrm{eff}}$= 0.2319 ± 0.0008(stat) ± 0.0018(syst) = 0.2319 ± 0.0019 is in good agreement with measurements ate⁺e⁻colliders.