The number of all possible values of Q is obtained as follows: (y + z) cos 3θ = (xy) sin θ (1) x sin 3θ =
2cos3θ
y
+
2sin3θ
z
(y + z) cos 3θ = (2 cos 3θ) z + (2 sin 3θ) y = (y + 2z) cos 3θ + y sin 3θ y (cos 3θ - 2 sin 3θ) = z cos 3θ and y (sin 3θ - cos 3θ) = 0 ⇒ sin 3θ - cos 3θ = 0 ⇒ sin 3θ = cos 3θ Therefore, 3θ = nπ+