fakatau (do something together) + kai (eat). fakatau- is a prefix indicating simultaneous action by two or more people (Ranby 1980). See also:
fakataupehe.
fakatau(一緒に行う)+ kai(食べる). fakatau- は2人以上の人が同時に行う行為を意味する接頭語(Ranby 1980). [参]
fakataupehe:一緒に歌う.