Tallbloke & cavortingcheetah
ETOPS does not have to mean flying continuously at MCT when you loose an engine.
It does mean targeting a higher TAS at a slightly lower altitude rather than MCT at max single engine altitude and step climbs maintaining MCT.
On an ETOPS diversion with an engine shut down, you descend to your ETOP's altitude at your ETOP's diversion speed and cruise at that speed (TAS). You may need MCT to start off with but as the weight reduces so does the thrust.
This is quicker and less demanding on the remaining engine than when operating at MCT at max single engine altitude, the cost is a little more fuel burn.
Of course engine failure is not the only thing that will cause an ETOP's diversion.