The number of solutions of the equation x + 2 tan(x) = π2 in the interval [0, 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: