In some circumstances the contribution of one neutrino flavor can be approximately neglected; e.g., in \(u_{\mu} \rightarrow u_{\tau}\) atmospheric oscillations the role played by the \(u_{e}\) is very small. Then the PMNS matrix reduces to a single \(2 \times 2\) matrix of the Cabibbo form with a single mixing angle, \(\theta\). Show that in this case (in natural units) we have \(P_{\ell, \ell^{\prime} ; \ell eq \ell^{\prime}}=\sin ^{2}(2 \theta) \sin ^{2}\left(\Delta m_{\ell \ell^{\prime}}^{2} L / 4 E\right)\).