Let f(x) = a₁ sin x + a₂ sin 2x + ∙ ∙ ∙ + a_n sin nx, where a₁, a₂ , . . . , an are real numbers and n is a positive integer. If it is given that |f(x)| ≤ |sin x| for all x, show that

|a₁ + 2a₂ + ∙ ∙ ∙ + na_n | ≤ 1