Let the vertices of △ABC be coinciding with the first, second and fourth vertices of a regular heptagon.
Find tan A + tan B + tan C.
(In reply to Solution
by Brian Smith)
To B. Smith
I sincerely hope you don't mind a bit of black humor. Your "elegant" solution brought to my mind a quote from the novel "The Heart of Darkness". The line is "The horror, the horror!"
In all fairness, I must admit that the answer -sqrt(7) has a poignant beauty with regard to a heptagon. (And is likely what DAK had in mind.)
But, I also think my tangents were OK and give the same result, but only just approximately. - Cheers SL