"He is not singing, even though he wants to."
Translation:Han sjunger inte, trots att han vill.
- "trots att" is like "in spite of", or "despite that".
- "även om" is like "even though".
- "fastän" is like "though", or "although".
So then, they all mean basically the same thing. It is just nuance, same as in English.
Gramatically though, "trots" is a preposition whereas the other two are conjunctions.
The det is optional, and the default translation actually doesn't have it. You should consider it a "that" rather than an "it", which makes more sense - "He is not singing, even though he wants that." Not very idiomatic in English, but perfectly normal in Swedish. :)
(Also, in case you're wondering, vill har is wrong because 1) vill is a modal so it would have been vill ha, and 2) vill ha is for nouns, vill is for verbs.)