  The dilepton azimuthal correlation, namely the difference $\phi$ between the
azimuthal angles of the positive and negative charged lepton in the laboratory
frame, provides a stringent test of the spin correlation in $t \bar t$
production at the Large Hadron Collider. We introduce a parameterisation of the
differential cross section $d\sigma / d\phi$ in terms of a Fourier series and
show that the third-order expansion provides a sufficiently accurate
approximation. This expansion can be considered as a `bridge' between theory
and data, making it very simple to cast predictions in the Standard Model (SM)
and beyond, and to report measurements, without the need to provide the numbers
for the whole binned distribution. We show its application by giving
predictions for the coefficients in the presence of (i) an anomalous top
chromomagnetic dipole moment; (ii) an anomalous $tbW$ interaction. The methods
presented greatly facilitate the study of this angular distribution, which is
of special interest given the $3.2(3.7)\sigma$ deviation from the SM
next-to-leading order prediction found by the ATLAS Collaboration in Run 2
data.
