Find all real solution of the equation sin^2x = -2+2cosx

Answer 1

since sin^2 = 1-cos^2,

1-cos^2 = -2 + 2cos
cos^2 + 2cos - 3 = 0
(cos+3)(cos-1) = 0

cos=1, so x = 0,2pi,4pi,...

why not -3?