1.
Let A=(cosθsinθ01)A = \begin{pmatrix} \cos\theta & \sin\theta \\ 0 & 1 \end{pmatrix} and P=(cosθsinθsinθcosθ)P = \begin{pmatrix} \cos\theta & \sin\theta \\ -\sin\theta & \cos\theta \end{pmatrix}. If B=PAPTB = PAP^{T} and C=PTB10PC = P^{T}B^{10}P, and the sum of the diagonal elements of CC is mn\dfrac{m}{n} with gcd(m,n)=1\gcd(m, n) = 1, then m+nm + n is: