The question is about this problem (it is from a Math' Olympiad in Germany):
Prove that if a regular heptagon $ABCDEFG$ has side 1, then
I have found something: using the law of cosines I have derived a third degree equation that is satisfied if the statement is true, but this solution is long and ugly, and, in fact, it is not a solution since the equation has two more roots. I can search for my notes if anybody would need details.
In fact, I'm looking for a less algebraic kind of solution :-)