Let A = [1/(√ 2), -2; 0, 1] and P = [cos θ, - sin θ; sin θ, cos θ], θ>0. If B = PAP^T, C = P^T B^10 P and the sum of the diagonal elements of C is…

Let $\displaystyle \mathrm{A}=\left[\begin{array}{cc}\frac{1}{\sqrt{2}} & -2 \\ 0 & 1\end{array}\right]$ and $\displaystyle \mathrm{P}=\left[\begin{array}{cc}\cos \theta & -\sin \theta \\ \sin \theta & \cos \theta\end{array}\right], \theta>0$. If $\displaystyle \mathrm{B}=\mathrm{PAP}^{\mathrm{T}}, \mathrm{C}=\mathrm{P}^{\mathrm{T}} \mathrm{B}^{10} \mathrm{P}$ and the sum of the diagonal elements of $\displaystyle C$ is $\displaystyle \frac{m}{n}$, where $\displaystyle \operatorname{gcd}(m, n)=1$, then $\displaystyle m+n$ is :