A multivariate likelihood method to measure electroweak couplings with the Drell-Yan process at the LHC is presented. The process is described by the dilepton rapidity, invariant mass, and decay angle distributions. The decay angle ambiguity due to the unknown assignment of the scattered constituent quark and antiquark to the two protons in a collision is resolved statistically using correlations between the observables. The method is applied to a sample of dimuon events from proton-proton collisions at √s=7TeV collected by the CMS experiment at the LHC, corresponding to an integrated luminosity of 1.1fb -1. From the dominant uū, dd̄→γ */Z→μ -μ + process, the effective weak mixing angle parameter is measured to be sin2θ eff=0.2287±0.0020(stat.)±0.0025(syst.). This result is consistent with measurements from other processes, as expected within the standard model. © 2011 CERN.