>>456
表記が面倒なので
s = sin(θ)
c = cos(θ)
とする。
s - c = 1/3
s^2 +c^2 =1
sin(3θ) + cos(3θ) = 3s-4s^3 -3c+4c^3
= (c-s)(4s^2 + 4c^2 + 4cs-3)
= -(1/3) (4 + 4cs-3)
= -(1/3) (4cs+1)

(s-c)^2 = 1/9
s^2 + c^2 -2sc = 1/9
2sc = 8/9