Let |M| denote the determinant of a square matrix M. Let g:[0,π/2]→ℝ be defined by g(θ)=√(f(θ)−1)+√(f(π/2−θ)−1), where f(θ) is the one-half multiple of the first 3×3 determinant plus the second 3×3 determinant printed below. Let p(x) be a quadratic polynomial whose roots are the maximum and minimum values of g(θ), and p(2)=2−√2. Then, which of the following is/are TRUE?