We report on the first measurement of the angular distributions of final state electrons in pp→γ∗/Z→e+e−+X events produced in the Z boson mass region at s√=1.96  TeV. The data sample collected by the CDF II detector for this result corresponds to 2.1  fb−1 of integrated luminosity. The angular distributions are studied as a function of the transverse momentum of the electron-positron pair and show good agreement with the Lam-Tung relation, consistent with a spin-1 description of the gluon, and demonstrate that, at high values of the transverse momentum, Z bosons are produced via quark-antiquark annihilation and quark-gluon Compton processes.