This is sentence:
「“見る”か。お前はいったい、どのような世界を“見て”いるのだろうな」
I'm not sure if this is really a question, but words like いったい and どのよう suggest that it probably is. So if this is really a question, then how should I inerpret だろう at the end, because usually as far as I know it represents information about which speaker thinks its almost certainly is true.
But here, it looks like question is in form of something like "In which way did you see world?", and I don't understand how だろう fits here.