A circle, centre \(O\), has \(AB\) as a diameter. Let \(C\) be a point on the circle different from \(A\) and \(B\), \(D\) be the point on \(AB\) such that \(\angle CDB = 90^{\circ}\) and \(M\) be the point on \(BC\) such that \(\angle BMO = 90^{\circ}\). \(DM\) is \(3 \times OM\). If \(\angle ABC\) can be expressed as \(\tan^{-1} (\frac{a}{b})\) where \(a\) and \(b\) are co-prime positive integers, determine \(a+b\).

Inspiration.