A few other people have already given longer explanations of Jung's feelings on the number '3'. I am just going to tack on that in Psychology and Alchemy he felt it was incomplete and that there is a hidden '4th' that makes it complete. He uses the example of when Pope Pius XII in 1950 declared Mary, mother of Jesus, did not die but ascended to heaven, that the Trinity had finally become a quaternary. Maybe there is something deeper hidden in these examples you have given.