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\subsubsection{Two flavor oscillations}
Since $U_{\alpha \beta} is a unitary matrix, in the case of two flavor oscillations, it can be represented by a rotation matrix
\begin{equation}
U_{\alpha \beta} = \begin{bmatrix}
\cos \theta & \sin \theta \\
-\sin \theta & \cos \theta \\
\end{bmatrix}
\end{equation}