[rodelrod]

"Aigu" does not take a trema. The feminine form "aigüe" does, and the trema is there because otherwise you'd pronounce it "/ɛɡ/" instead of "/ɛ.ɡy/". It does not change the sound of the "u" at all.

[smorrebrod]

To add to the strangeness of it all, "aigüe" used to be incorrect and "aiguë" was correct. Since it does not make sense now both words are correct.