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Ravi wants to trisect an angle AOB, which has measure θ. 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∠DOB=∠DOA, so OD will trisect angle AOB. What is the sum of all angles θ with 0∘<θ<90∘, such that his claim is true?

is it 45?

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