I've looked at this before. I don't recall it being direct. I think it had at least 1 stop and was often part of a code share. Things may have changed though.I understand that AirNZ has flights to LAX to/from Rarotonga. Has anyone ever tried this? Seems like it would make a nice weekend stop!
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The other answer is JL via Tokyo... it's a little over $6k year round in J.