  High precision data of lepton angular distributions in inclusive $Z$ boson
production, reported by the CMS and ATLAS Collaborations, showed pronounced
transverse momentum ($q_T$) dependencies of the $A_0$ and $A_2$ coefficients.
Violation of the Lam-Tung relation, $A_0 = A_2$, was also found. An intuitive
understanding of these results can be obtained from a geometric approach. We
predict that $A_0$ and $A_2$ for $Z$ plus single gluon-jet events are very
different from that of $Z$ plus single quark-jet events, allowing a new
experimental tool for checking various algorithms which attempt to discriminate
quark jets from gluon jets. We also predict that the Lam-Tung relation would be
more severely violated for the $Z$ plus multiple-jet data than what has been
observed so far for inclusive $Z$ production data. These predictions can be
readily tested using existing LHC data.
