  We report on the first measurement of the angular distributions of final
state electrons in $p\bar{p}\to \gamma^{*}/Z\to e^{+}e^{-}+X$ events produced
in the $Z$ boson mass region at $\sqrt{s}=1.96$ 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 anti-quark annihilation and quark-gluon Compton processes.
