  We apply torque equilibrium spin wave theory (TESWT) to investigate an
anisotropic XXZ antiferromagnetic model with Dzyaloshinskii-Moriya (DM)
interaction in a triangular lattice. Considering the quasiparticle vacuum as
our reference, we provide an accurate analysis of the non-collinear ground
state of a frustrated triangular lattice magnet using the TESWT formalism. We
elucidate the effects of quantum fluctuations on the ordering wave vector based
on model system parameters. We study the single magnon dispersion, the
two-magnon continuum using the spectral function, and the Raman spectrum of
bimagnon and trimagnon excitations. We present our results for the $HH, VV$,
and the $HV$ polarization Raman geometry dependence of the bimagnon and the
trimagnon excitation spectrum where $H (V)$ represents horizontal (vertical)
polarization. Our calculations show that both the $HH$ and the $HV$
polarization spectrum can be used to determine the degree of anisotropy of our
system. We calculate the Raman spectra of Ba$_3$CoSb$_2$O$_9$ and
Cs$_2$CuCl$_4$.
