  The semiclassical Lifshitz-Kosevich-type description is given for the angular
dependence of quantum oscillations with combination frequencies in a multiband
quasi-two-dimensional Fermi liquid with a constant number of electrons. The
analytical expressions are found for the Dingle, thermal, spin, and amplitude
(Yamaji) reduction factors of the novel combination harmonics, where the latter
two strongly oscillate with the direction of the field. At the "magic" angles
those factors reduce to the purely two-dimensional expressions given earlier.
The combination harmonics are suppressed in the presence of the non-quantized
("background") states, and they decay exponentially faster with temperature
and/or disorder compared to the standard harmonics, providing an additional
tool for electronic structure determination. The theory is applied to
Sr$_2$RuO$_4$.
