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In this paper a general method to measure the longitudinal polarization of$\tau$ lepton in the process $pp \rightarrow Z^{0} \rightarrow \tau\tau$ isdescribed. The method of optimal observable allows to distinguish between the$\tau$ lepton helicity states with maximum possible sensitivity. The optimalobservable for the main $\tau$ decay modes ($e/\mu\nu\nu$, $\pi\nu$, $\rho\nu$,$a_{1}\nu$) that can be identified by CMS or ATLAS detectors is described. Theanalyzing power for $\tau$ polarization can be further gained by taking intoaccount a correlation between longitudinal spin states of $\tau^{+}$ and$\tau^{-}$. The theoretical systematic uncertainty on the $\tau$ polarizationmeasured using the $\tau \rightarrow 3\pi\nu$ decays is estimated to be$(\Delta P_{\tau})_{model} = (1.41 \pm 1.37)\times 10^{-4}$. This value isapproximately 50 times smaller than the best uncertainty on $\tau$ polarizationmeasurement given by combination of all LEP results. An approach to propagatethe measured $\tau$ polarization averaged over the $Z^{0}$ lineshape and partondensity functions to the electroweak parameters is also discussed.

Methods for a measurement of $\tau$ polarization asymmetry in the decay  $Z\rightarrow \tau\tau$ at LHC and determination of the effective weak mixing  angle