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We present a solution to the strong CP problem based on spontaneous CPviolation and discrete family symmetries. The model predicts in a natural waythe almost right-angled quark unitarity triangle angle ($\alpha \simeq90^\circ$) by making the entries of the quark mass matrices either real orimaginary. By this choice the determinants of the mass matrices are renderedreal and hence the strong CP phase vanishes. We present a toy model for thequark sector that demonstrates the viability of our approach.

Solving the Strong CP Problem with Discrete Symmetries and the Right Unitarity Triangle