Ga-71 and Ga-69 single-crystal MMR spectra of a beta-Ga2O3 twin have been analyzed in terms of the Ga-71/Ga-69 quadrupole coupling and chemical shielding anisotropy (CSA) interactions. Analyses of the magnitudes and orientations of the interaction tensors for the two distinct crystallographic gallium sites in the two twin crystals resulted in accurate values for the parameters describing the quadrupole coupling and CSA tensors. Moreover, it has been possible to determine the actual twin-law of our sample crystal. Along with a recent Ga-71 Single-crystal NMR investigation of YGG, this work shows that gallium CSA generally has to be taken into account in addition to the dominant quadrupole coupling interaction.