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Fiji Airways is offering flights for $972 via Nadi to Los Angeles for various dates until June. Alternatively, Hawaiian Airlines is offering some $923 fares return with a stopover in Honolulu. The next best prices are ~$1252 with United and $1500 with Air NZ.
The Hawaiian Airlines flights are for select dates between October - January with flights ranging from $923, $947 and $953. There should be other dates for around $999 between Jan-April according to STA Travel.
Skyscanner showing the $923 Flight
The Fiji Airways $972 flight is via STA travel (screenshot). Dates: October 2016 – June 2017
Use Skyscanner to find a calendar of the cheapest flights.
Via Fly4Free