The document finds the angle a that satisfies the identity 2sin^2a - sina - 1 = 0. It uses substitution to rewrite the equation in terms of t = sin a, resulting in a quadratic equation. The quadratic formula yields the solutions t1 = 1 and t2 = -1/2. Substituting these back gives the angle solutions as a = (-1)^k*(π/2) + kπ or a = (-1)^(k+1)*(π/6) + kπ.