# Trisecting an angle

Geometry Level 5

Ravi wants to trisect an angle $$AOB$$, which has measure $$\theta$$. From $$A$$, he drops a perpendicular to side $$OB$$, intersecting at $$C$$. He then constructs an equilateral triangle $$ACD$$ on the opposite side of $$AC$$ as compared to $$O$$. He claims (without any justification) that $$2\angle DOB = \angle DOA$$, so $$OD$$ will trisect angle $$AOB$$. What is the sum of all angles $$\theta$$ with $$0 ^\circ < \theta < 90^\circ$$, such that his claim is true?

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