  Context. As of today, asteroseismology mainly allows us to probe the internal
rotation of stars when modes are only weakly affected by rotation using
perturbative methods. Such methods cannot be applied to rapidly rotating stars,
which exhibit complex oscillation spectra. In this context, the so-called
traditional approximation, which neglects the terms associated with the
latitudinal component of the rotation vector, describes modes that are strongly
affected by rotation. This approximation is sometimes used for interpreting
asteroseismic data, however, its domain of validity is not established yet.
  Aims. We aim at deriving analytical prescriptions for period spacings of
low-frequency gravity modes strongly affected by rotation through the full
Coriolis acceleration, which can be used to probe stellar internal structure
and rotation.
  Methods. We approximated the asymptotic theory of gravito-inertial waves in
uniformly rotating stars using ray theory described in a previous paper in the
low-frequency regime, where waves are trapped near the equatorial plane. We put
the equations of ray dynamics into a separable form and used the EBK
quantisation method to compute modes frequencies from rays.
  Results. Two spectral patterns that depend on stratification and rotation are
predicted within this new approximation: one for axisymmetric modes and one for
non-axisymmetric modes.
  Conclusions. The detection of the predicted patterns in observed oscillation
spectra would give constraints on internal rotation and chemical stratification
of rapidly rotating stars exhibiting gravity modes, such as $\gamma$ Doradus,
SPB, or Be stars. The obtained results have a mathematical form that is similar
to that of the traditional approximation, but the new approximation takes the
full Coriolis, which allows for propagation near the centre, and centrifugal
accelerations into account.
