Drell-Yan lepton pairs are produced in the process pp¯→e+e−+X through an intermediate γ∗/Z boson. The lepton angular distributions are used to provide information on the electroweak-mixing parameter sin2θW via its observable effective-leptonic sin2θW, or sin2θlepteff. A new method to infer sin2θW or, equivalently, the W-boson mass MW in the on-shell scheme, is developed and tested using a previous CDF Run II measurement of angular distributions from electron pairs in a sample corresponding to 2.1 fb−1 of integrated luminosity from pp¯ collisions at a center-of-momentum energy of 1.96 TeV. The value of sin2θlepteff is found to be 0.2328±0.0011. Within a specified context of the standard model, this results in sin2θW=0.2246±0.0011, which corresponds to a W-boson mass of 80.297±0.055 GeV/c2, in agreement with previous determinations in electron-position collisions and at the Tevatron collider.