sin3x - 3sin2x - cos2x + 3sinx + 3cosx - 2 = 0
⇔ 3sinx - 4sin³x - 3sin2x + 3sinx - cos2x + 3cosx - 2 = 0
⇔ sinx(3 - 4sin²x) - 6sinx.cosx + 3sinx - 2cos²x + 3cosx - 1 = 0
⇔ sinx(4cos²x - 1) - 3sinx(2cosx - 1) - (2cosx - 1)(cosx - 1) = 0
⇔ sinx(2cosx - 1)(2cosx + 1) - 3sinx(2cosx - 1) - (2cosx - 1)(cosx - 1) = 0
⇔ (2cosx - 1)(2sinx.cosx + sinx - 3sinx - cosx + 1) = 0
⇔ (2cosx - 1)(2sinx.cosx - 2sinx - cosx + 1) = 0
⇔ (2cosx - 1)(cosx - 1)(2sinx - 1) = 0
. . .[ cosx = 1/2 → x = ± π/3 + k2π (k ∈ Z)
⇔ [ cosx = 1 → x = k2π (k ∈ Z)
. . .[ sinx = 1/2 → x = π/6 + k2π hoặc x = 5π/6 + k2π (k ∈ Z)