For what values of λ does the equation λ cos 2x2 cos 2x - 1 = λ + sin x(cos2 x - 3 sin2 x) tan x have real solutions?

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: