  The angular moments for the $Z$ boson can be used as analyzers for the
underlying production dynamics for the $t\bar t Z$ and $t Zj$ processes. In
this manuscript, we derive these angular moments at leading and next-to-leading
order in QCD at the LHC. We show that these observables work as efficient
probes to beyond the Standard Model effects, considering the Standard Model
Effective Field theory framework. Remarkably, we observe that these probes
unveil blind directions to CP-odd operators, providing sizable new physics
sensitivity at the 14 TeV LHC with 3 ab$^{-1}$ of data.
