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Question:

Let S = {θ ∈ [-2π, 2π] : 2cos2θ + 3sinθ = 0}. Then the sum of the elements of S is?

π

5π/3

13π/6

2π

Solution:

2(1 - sin²θ) + 3sinθ = 0 ⇒ 2sin²θ - 3sinθ - 2 = 0 ⇒ (2sinθ + 1)(sinθ - 2) = 0 ⇒ sinθ = -1/2, sinθ = 2 (reject)
Roots: π + π/6, 2π - π/6, -π/6, -π + π/6 ⇒ sum of values = 2π.