[Gryphin]

Another possible option:
1) Go into defensive posture or make peace wiht other enemys, (Economy of Force).
2) Acertain what kinds of Ships / Weapons would be best to use against the EEE.
3) Build a suitable invasion force with the intent to capture planets. (You will need the resources later)
4) Trade with the EEE for what ever Mineral / Organic / Radioactive you will need a surplus of to build the fleet. Always offer about 5% more of what you do not need.
5) Assemble the fleet and move very quickly. (3 or more fleets with at least two transports each)
6) Note your score and EEE's score before you declare war.
Reason for these precaustions:
The EEE are frequently the 1st or 2nd most poswerful AI, Taking them out could propell you into Mega Evil Empire status befor you are ready.

I personaly would never do this, (twice), but it dose work.