Let (x) = a 1 sin x + a 2 sin 2x + ...+ a n sin nx, where a 1 , a 2 ,...,

Let ƒ(x) = a₁ sin x + a₂ sin 2x + ...+ a_n sin nx, where a₁, a₂,..., a_n are real numbers and where n is a positive integer. Given that |ƒ(x)| ≤ sin x| for all real x, prove that |a₁ + 2a₂ + · · · + na_n| ≤ 1.