Why dha throigh, but se troithe? I feel like I should know, but I don't.
troigh is one that has an irregular counting form, like bliain, uair and sechtain.
We haven't explained this fully in the notes. Nine nouns use a special plural form when counting with bunuimhreacha, and tróigh is one of them - but the special plural is not used for one or two.
A summary of the special rules for troigh and friends can be found in the discussion here.