It seems kind of crazy that they would visit the Greeks, then do another flyby of Earth in order to visit the Trojans. I wonder what the cost-benefit analysis was of doing that versus just sending separate probes to each of those (which presumably would need a lot less fuel)? Is this one of those things where this really is the best and cheapest option and my intuition of orbital mechanics is just wrong?
The flybys provide course changes for very little fuel, including pretty significant velocity boosts. It's not uncommon for a probe to spend a while ping-ponging around the inner system just to get enough speed to reach the outer planets. I doubt the probe has a whole lot of delta-v left once it leaves Earth the first time, probably just enough for course corrections so it can hit the flybys precisely.