Originally Posted by nako

No - the OP can take a shuttle directly from the Eagle terminal to Terminal 3. In fact, these shuttles can be used with relative ease to do a T3-to-T4 (or vice versa) transfer, with the intermediate stop at the Eagle terminal to switch shuttles. As long as you have boarding passes or an itinerary reflecting the need to go from one terminal to another, there is no problem with doing this type of transfer.

Mike