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 sqrt(s) = 7 TeV collected by the CMS experiment at the LHC, corresponding to an integrated luminosity of 1.1 inverse femtobarns. From the dominant u-ubar, d-dbar to gamma*/Z to opposite sign dimuons process, the effective weak mixing angle parameter is measured to be sin^2(theta[eff]) = 0.2287 +/- 0.0020 (stat.) +/- 0.0025 (syst.). This result is consistent with measurements from other processes, as expected within the standard model.