  Magnetoresistivity features connected with the spin level coincidences under
tilted fields in a $\Gamma_8$ conduction band of the HgTe quantum well were
found to align along straight trajectories in a $(B_\bot,B_{||})$ plane between
the field components perpendicular and parallel to the layer meaning a linear
spin polarization dependence on magnetic field. Among the trajectories is a
noticeable set of lines descending from a single point on the $B_{||}$ axis,
which is shown to yield a field of the full spin polarization of the electronic
system, in agreement with the data on the electron redistribution between spin
subbands obtained from Fourier transforms of oscillations along circle
trajectories in the $(B_\bot,B_{||})$ plane and with the point on the
magnetoresistivity under pure $B_{||}$ separating a complicated weak field
dependence from the monotonous one. The whole picture of coincidences is well
described by the isotropic $g$-factor although its value is twice as small as
that obtained from oscillations under pure perpendicular fields. The
discrepancy is attributed to different manifestations of spin polarization
phenomena in the coincidences and within the exchange enhanced spin gaps. In
the quantum Hall range of $B_\bot$, the spin polarization manifests in
anticrossings of magnetic levels, which were found to depend dramatically
nonmonotonously on $B_\bot$.
