The number of solutions of √3 cos(2θ) + 8 cos(θ) + 3√3 = 0 for θ ∈ [-3π, 2π] is:

If 3 sin2(t) - 12 sin(t) - 3 = p, then the sum of all integral values of 'p' such that the equation has at least one real root is:

Let x ∈ [−π, π] and S = {x : sin x(sin x + cos x) = a, a ∈ &bold;Z&bold;}. Then the number of elements in set S is equal to: