Chameleons at Dusk

A secluded colony contains 45 chameleons: 13 are red, 15 are green, and 17 are blue. Whenever two chameleons of different colours meet, they both immediately change to the third colour. For example, a red chameleon meeting a green one causes both to become blue. Meetings between two chameleons of the same colour have no effect. The chameleons may meet in any order, and the process may continue for as many meetings as desired. Is there any sequence of meetings that eventually leaves all 45 chameleons the same colour?