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