# You'll like to calculate it!

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 $$\angle BMO = 90^{\circ}$$. $$DM$$ 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 $$a+b$$.

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