In a triangle ABC, if a, b, and c are the lengths of the sides opposite to the angles A, B, and C respectively, then what is sin(A - B)sin(A + B) equal to?

In a triangle ABC, if sin(A) = cos(B) + cos(C), then what is tan(B2) + cot(B2) equal to?

In a ΔABC, vertex A ≡ (1, 2), the midpoint of side AB is (-5, -1), and the centroid of the triangle is (3, 4). If the circumcentre is (α, β), then the value of 21(α + β) is: