If I suspect I have "the," I look through the puzzle for the "th" combination, since it's the most common 2-letter sequence in the language. If I find some, I am more sure I have it right.
A 4 letter word with the middle two letters the same usu. means that the middle letters are "e" or "o". I have never run across a word like this where that's not the case. If calling it 'e' gives you something like a two-letter gibberish word that starts with "e," for example, then you can be sure it's "o."