In the Standard Model, the charged weak interaction is described by the Cabbibo-Kobayashi-Maskawa (CKM) matrix. The one of the central goals of flavour-physics experiments is to determine the angles alpha, beta and gamma of the b-d CKM unitary triangle precisely. The BPGGSZ formalism for measuring gamma using the decay B- ->DK-, where D represents either a D0 or D0bar, utilises self-conjugate mutibody final states such as K0Sh+h- (h=k,pi). However, a model-independent measurement of gamma using this mode requires the knowledge of the strong-phase difference between the D0 and D0bar meson decay amplitudes. We present a measurement of the strong-phase difference between D0 and D0bar-> K0SK+K- performed through a study of quantum-correlated pairs of charm mesons. Using 2.93 fb^−1 of e+e− collision data collected with the BESIII detector corresponding to the mass of the psi(3770) resonance, we employ a binned Dalitz-plot analysis of D0->K0SK+K- and of D0->K0LK+K- decays recoiling against flavor-tagged, CP-tagged, and K0S K+K- - tagged events to determine these strong-phase differences. This is the most precise measurement to date of the strong-phase difference in these decays. Using these parameters, the associated uncertainty on the gamma is expected to be between 1.3^deg and 2.3^deg for an analysis using the decay B- ->D(K0SK+K-)K-. These results presented here are also important for the model-independent determination of charm-mixing and CP violation in D mesons.