We point out that the measurement of just the two branching fractions
B(K+ --> pi+nunuBAR) and B(K(L) --> pi0nunuBAR) can in a theoretically
clean manner determine sin 2beta almost independently of m(t) and V(c
b). This allows to obtain an interesting relation between the CP asymm
etry A(CP)(psiKs) in B physics and the branching ratios for these two
rare K decays. The recently calculated next-to-leading order QCD corre
ctions improve the accuracy of this analysis. We find typically DELTA
sin 2beta = +/-0.11 provided B(K+ --> pi+nunuBAR) and B(K(L) --> pi0nu
nuBAR) are measured within +/-10% accuracy. With decreasing uncertaint
y in LAMBDA(MSBAR) and m(c) this error could be reduced to DELTA sin 2
beta < +/-0.10. The determination of sin2alpha and sin2gamma on the ot
her hand is rather poor. However respectable determinations of the Wol
fenstein parameter eta and of \V(td)\ can be obtained.