sinα=cos2α=1-2sin^2α
2sin^2α + sinα - 1 = 0
(sinα+1)(2sinα-1）=0
α∈[π/2,π],sinα＞0,sinα+1＞1
2sinα-1=0
sinα=1/2
tanα = -sinα/√(1-sin^2α) = -√3/3