The book reports a joint analysis between the LHCb and BESIII collaborations on measuring the CKM angle ? with intricate data analysis techniques and rigorous statistical methods. Based on a proposal of an unbinned BPGGSZ method with Fourier expansion, a novel approach is developed. Applying an optimised weighting function across the Dalitz plot, deduced from the decay amplitude and background level in data, the statistical uncertainty of ? may effectively be improved compared to the current analyses. The feasibility of the approach is proven by tests with pseudo-data generated according to previous experimental measurements. Applying this approach to the data collected by the LHCb and BESIII experiments to measure the CKM angle ?, the preliminary result obtained has a significantly lower statistical uncertainty than previous measurements. The new approach developed in the thesis provides an important and extremely valuable addition to test the CKM mechanism.