  We compute the K-edge indirect resonant inelastic x-ray scattering (RIXS)
spectrum of a triangular lattice antiferromagnet in its ordered coplanar 3-
sublattice 120 degree magnetic state. By considering the first order
self$-$energy corrections to the spin wave spectrum, magnon decay rate,
bimagnon interactions within the ladder approximation Bethe-Salpeter scheme,
and the effect of three-magnon contributions up to 1/S- order we find that the
RIXS spectra is non-trivially affected. For a purely isotropic triangular
lattice model, the peak splitting mechanism and the appearance of a multipeak
RIXS structure is primarily dictated by the damping of magnon modes. At a
scattering wavevector corresponding to the zone center \Gamma point and at the
roton point q=M, where the magnon decay rate is zero, a stable single peak
forms. At the $\Gamma$ point, the contribution is purely trimagnon at the 1/S
level and occurs approximately at the trimagnon energy of 6JS. The roton peak
occurs at a lower energy of 4JS. The K-edge single peak RIXS spectra at the
roton momentum can be utilized as an experimental signature to detect the
presence of roton excitations. A unique feature of the triangular lattice
K-edge RIXS spectra is the nonvanishing RIXS intensity at both the zone center
$\Gamma$ point and the antiferromagnetic wavevector K point. This result is in
sharp contrast to the vanishing K-edge RIXS intensity of the collinear magnetic
phases on the square lattice. We find that including XXZ anisotropy leads to
additional peak splitting, including at the roton scattering wavevector where
the single peak destabilizes towards a two-peak structure. The observed
splitting is consistent with our earlier theoretical prediction of the effects
of spatial anisotropy on the RIXS spectra of a frustrated quantum magnet [Luo,
Datta, and Yao, Phys. Rev. B 89, 165103 (2014)].
