Let \( A = \begin{bmatrix} \frac{1}{\sqrt{2}} & -2 \\ 0 & 1 \end{bmatrix} \) and \( P = \begin{bmatrix} \cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{bmatrix}, \theta \geq 0. \) If \( B = PAP^T, C = P^TB^TP \) and the sum of the diagonal elements of \( C \) is \( \frac{m}{n} \), where \( \gcd(m, n) = 1 \), then \( m + n \) is