Let () = 2 sin 2 + sin 4. (a) Show that is a critical point if cos 4 = cos 2. (b)

Let ƒ(θ) = 2 sin 2θ + sin 4θ.
(a) Show that θ is a critical point if cos 4θ = − cos 2θ.
(b) Show, using a unit circle, that cos θ₁ = − cos θ₂ if and only if θ₁ = π ± θ₂ + 2πk for an integer k.
(c) Show that cos 4θ = − cos 2θ if and only if θ = π/2+ πk or θ = π/6 +(π/3)k.
(d) Find the six critical points of ƒ on [0, 2π] and find the extreme values of ƒ on this interval.
(e) Check your results against a graph of ƒ.