Let \(\omega\) be the circumcircle of a triangle \(\triangle ABC.\) A line \(\ell\) passing through point \(A\) intersects segment \(BC\) and \(\omega\) at points \(P,Q\) respectively (where \(Q \neq A\)). Let \(O\) be the circumcenter of \(\triangle BPQ,\) and let \(AO\) intersect \(BC\) at \(K.\) Given that \(O\) lies on \(\omega,\) find \(\angle AKB \) in degrees.

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