I refer to this question.
Basically it asks for a proof of a known result, without using a very general & basic formula. The question has received a decent amount of views and there seemed to be a common approval from all comments that the answer should probably be "No".
The question is only a week old, so someone might still find a positive answer, but this is starting to feel quite unlikely.
How should such a question be dealt with ? Should it stay open as long as no positive answer is found? or should someone just basically answer "Very unlikely - not possible as far as I (or MSE community) knows"
Edit - 06/11 This post has now an accepted answer. The piece of mathematics used is very interesting and well done. I'm still unsure if this answers perfectly the question, because (as mentioned in the answer) it is very close to reproving Euler's formula. But that's only my opinion. The general question on how we should treat these cases is still interesting I think.