The excitation energies of the four lowest-lying singlet excited states of the TiO2, Ti2O4, and Ti3O6 clusters are calculated by a variety of different Equation-of-Motion Coupled Cluster (EOM-CC) approaches in order to obtain benchmark values for the optical excitations of titanium dioxide clusters. More specifically we investigate what the effect is of the inclusion of triple excitations "triples" in the (EOM-)CC scheme on the calculated excited states of the clusters. While for the monomer and dimer the inclusion of triples is found to only cause a rigid shift in the excitation energies, in the case of the trimer the crossing of the excited states is observed. Coupled cluster approaches where triples are treated perturbatively were found to offer no advantage over EOM-CCSD, whereas the active-space methods (EOM-CCSDt(II/I)) were demonstrated to yield results very close to full EOM-CCSDT, but at a much reduced computational cost.