Specific features in the formation of Landau levels in a three-dimensional topological insulator based on an 80-nm-thick strained mercury telluride film in an inclined magnetic field are studied. The magnetoresistance in the Hall bar geometry with a gate is measured at a temperature 1.9 K and in an applied magnetic field up to 10 T. The gate allows varying the Fermi level position from the valence to conduction band, passing through the bulk band gap. The samples are mounted on a rotating platform that makes it possible to change arbitrarily the angle between the magnetic field direction and the normal to the sample plane within the range of 0°–90°. It is found that the Shubnikov–de Haas oscillations are formed if the perpendicular magnetic field component exceeds 0.4 T, independent of the applied gate voltage. However, the sensitivity of the system to the parallel magnetic field component exhibits a pronounced dependence on the applied gate voltage. Namely, if the Fermi level is in the bulk band gap and the conductivity is determined by the surface states, the amplitude and position of Shubnikov–de Haas oscillations remain independent of the perpendicular magnetic field component even in the situation where the parallel component is twice as large as the perpendicular one. At high magnetic fields, the amplitude of oscillations is suppressed by the parallel field component. On the contrary, if the Fermi level is in the valence or conduction band, the parallel field component not only affects the amplitude of oscillations but also results even in their qualitative changes, e.g., giving rise to new minima related to Zeeman splitting. The observed behavior of the system is in agreement with the modern concepts concerning the spin polarization of the surface state in three-dimensional topological insulators and the spin degeneracy of charge carriers in the bulk.