Let \( |M| \) denote the determinant of a square matrix \( M \). Let \( g:[0,\dfrac{\pi}{2}]\to \mathbb{R} \) be the function defined by \( g(\theta)=\sqrt{\,f(\theta)-1\,}+\sqrt{\,f\!\left(\dfrac{\pi}{2}-\theta\right)-1\,} \)
Let \( p(x) \) be a quadratic polynomial whose roots are the maximum and minimum values of the function \( g(\theta) \), and \( p(2)=2-\sqrt{2} \). Then, which of the following is/are TRUE?
