tan((π/12) - x), tan (π/12), tan((π/12) + x) in the order are the three consecutive terms of a GP then sum all the solutions in [0,314] is kπ. Find value of k.
I tried assuming
a = tan (π/12) and y = tanx to make my calculations easier.
a^2 = (a+y)/(1-ay) * (a-y)/(1+ay)
Simplifying this simple removes y from the expression. What should I do? Where am I missing.