Problem 2 - Entrance Test

Using the identity sin(5θ) = 16 sin⁵θ - 20 sin³θ + 5 sinθ. Setting this equal to 5 sinθ gives 16 sin⁵θ - 20 sin³θ = 0 ⇒ sin³θ(16 sin²θ - 20) = 0. Solutions where sinθ = 0 (θ = 0, π) and sin²θ = 20/16 = 5/4 (invalid). Only valid solution is θ = π. However, checking θ = π/2: sin(5*(π/2)) = sin(5π/2) = 1, 5 sin(π/2) = 5. Not equal. Final answer: θ = π.