Let | M | denote the determinant of a square matrix M . Let g: [0, 2 ] R be the function…

Let |M| denote the determinant of a square matrix M.
Let \(g:\left[0, \frac{\pi}{2}\right] \rightarrow R\) be the function defined by
\(g(\ heta)=\sqrt{f(\ heta)-1}+\sqrt{f\left(\frac{\pi}{2}-\ heta\right)-1}\)
where, \[f(\ heta)=\frac{1}{2}\left|\begin{array}{ccc} 1 & \sin \ heta & 1 \\ -\sin \ heta & 1 & \sin \ heta \\ -1 & -\sin \ heta & 1 \end{array}\right|\]

Let p(x) be a quadratic polynomial whose roots are the maximum and minimum values of the function g(θ), and . Then, which of the following is/are true?