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The study of the interplay between topology and magnetism has begun to show a plethora of candidate materials where magnons can be classified as topological (arxiv:2206.06248). One recent example of a potential topological magnetic material is CoTiO₃. We use a combination of time domain THz (TDTS) and magneto-Raman spectroscopies to measure the low energy magnetic spectrum in CoTiO₃ and detect the two lowest energy magnons, one of which is the gapped Goldstone mode which responds to THz magnetic field perpendicular to the honeycomb plane, and the other is an inversion even optical magnon which is active for THz magnetic field parallel to the honeycomb plane. We build a theoretical model that can explain the opening of the gap of the pseudo Goldstone magnon and the magnetic field dependence of the two magnons with the apperance of a small ring exchange interaction between 6 spins in a hexagonal plaquette. This study shows the power of combining TDTS and Raman spectroscopies with theoretical modeling to understand the nature of the magnetic excitations in quantum magnets.