Local content of bipartite qubit correlations

One of the last open problems concerning two qubits in a pure state is to find the exact local content of their correlation, in the sense of Elitzur, Popescu, and Rohrlich (EPR2) [A. C. Elitzur, S. Popescu, and D. Rohrlich, Phys. Lett. A162, 25 (1992)]. We propose an EPR2 decomposition that allows us to prove, for a wide range of states $|\ensuremath{\psi}(\ensuremath{\theta})\ensuremath{\rangle}=\mathrm{cos}\ensuremath{\theta}|00\ensuremath{\rangle}+\mathrm{sin}\ensuremath{\theta}|11\ensuremath{\rangle}$, that their local content is $\overline{{p}_{L}}(\ensuremath{\theta})=\mathrm{cos}2\ensuremath{\theta}$. We also share reflections on how to possibly extend this result to all two-qubit pure states.