Can you do this without trigonometry?

Geometry Level 4

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 \(\angle BMO = 90^{\circ}\). If \(DB\) is \(3 \times OM\), calculate \(\angle ABC\) in degrees.

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