We can write \(\begin{bmatrix} 3 & 2 \\ 2 & 3 \end{bmatrix}\) as \(U D U^\mathsf{T}\) where \(U = \begin{bmatrix} \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} & -\frac{1}{\sqrt{2}}\end{bmatrix}\) and \(D = \begin{bmatrix} a & 0 \\ 0 & b\end{bmatrix}\). What is \(a + b\)?