Theory of CP angles measurements

In the early 80’s Sanda-san and collaborators wrote key papers on the direct and clean determination of the unitarity angle φ1 (β). This motivated many of us for analogously coming up with ways for direct and clean determinations of the other two unitarity angles, φ2(α) and φ3(γ). Current status of these direct determinations as well as our expectations for when Belle-II has 50 ab−1 of luminosity and LHCb with some upgrades, will be given. In particular, it is emphasized that for direct determination of φ3, Belle-II should be able to handle final states in D0 or $\bar{D}^0$ Dalitz decays, that contain one π0 (which are difficult for LHCb) then they may make further inroads in improving the accuracy of φ3 determination. Early lattice inputs for constraining the unitarity triangle (UT) are briefly recalled. Its crucial role in supporting the Kobayashi-Maskawa theory of CP violation is emphasized. Over the years lattice methods have made significant progress and latest constraints from these for the UT will be discussed as well as compatibility with current direct determinations and some comments on future outlook will be made.