In an equilateral triangle \( ABC \), point \( D \) is chosen on \( BC \) such that \( AD \) is the altitude of the triangle. Let the exterior angle at \( D \) formed by extending \( AD \) be \( \theta \). Given that the measure of \( \angle BAC \) is \( 60^\circ \), find the value of \( \theta \). Let's think step by step and output the final answer within \boxed{}.
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