In the wikipedia page about neutrino oscillation (or ate least in the current revision), the CP-asymmetry is written as $$A^{(\alpha\beta)}_{\text{CP}}=P(\nu_\alpha \rightarrow\nu_\beta)-P(\bar{\nu}_{\alpha}\rightarrow\bar{\nu}_{\beta}) =4\sum_{i>j}\mathrm{Im}\big(U^*_{\alpha i} U_{\beta i}U_{\alpha j} U^*_{\beta j}\big) \sin\Big(\tfrac{\Delta m^2_{ij}L}{2E}\Big)\tag{1}$$ where where $U$ is the neutrino mixing matrix with elements $U_{\alpha i}$. Here, $\alpha$ labels neutrino flavours ($e,\mu$ or $\tau$) and $i$ labels neutrino mass eigenstates such that $$|\nu_\alpha\rangle=\sum\limits_{i=1}^{3}U^*_{\alpha i}|\nu_i\rangle.$$
Now, the probability of oscillation from neutrino flavour $\alpha$ to flavour $\beta$ is given by$$ \begin{aligned}P_{\alpha\beta}=P(\nu_\alpha \rightarrow\nu_\beta)&=\delta_{\alpha\beta}- 4\sum\limits_{i>j} {\text{Re}}(U_{\alpha i}^{*} U_{\beta i} U_{\alpha j} U_{\beta j}^{*}) \sin^2(\Delta m_{ij}^2 L/4E)\\&+ 2\sum_{i>j}{\text{Im}}(U_{\alpha i}^{*}U_{\beta i}U_{\alpha j} U_{\beta j}^{*}) \sin(2\Delta m_{ij}^2 L/4E ),\end{aligned}\tag{2}$$ And the probability of oscillation from an antineutrino flavour $\alpha$ to flavour $\beta$ is given by $$ \begin{aligned}P(\bar{\nu}_{\alpha}\rightarrow\bar{\nu}_{\beta})&=P_{\alpha\beta}(U_{\alpha i}\to U^*_{\alpha i})\\&= \delta_{\alpha\beta}- 4\sum\limits_{i>j} {\text{Re}}(U_{\alpha i} U^*_{\beta i} U^*_{\alpha j} U_{\beta j}) \sin^2(\Delta m_{ij}^2 L/4E) \\&+ 2\sum_{i>j}{\text{Im}}(U_{\alpha i}U^*_{\beta i}U^*_{\alpha j} U_{\beta j}) \sin(2\Delta m_{ij}^2 L/4E),\end{aligned}\tag{3}.$$ Simple subtraction of (3) from (2), does not lead to Eq. (1). How is the formula Eq.(1) derived?
