(a) If a new trial is granted in the action the action shall again be brought to trial within the following times:
(1) If a trial is commenced but no judgment is entered because of a mistrial or because a jury is unable to reach a decision, within three years after the order of the court declaring the mistrial or the disagreement of the jury is entered.
(2) If after judgment a new trial is granted and no appeal is taken, within three years after the order granting the new trial is entered.
(3) If on appeal an order granting a new trial is affirmed or a judgment is reversed and the action remanded for a new trial, within three years after the remittitur is filed by the clerk of the trial court.
(b) Nothing in this section requires that an action again be brought to trial before expiration of the time prescribed in Section 583.310.