Given a circle with equation \(x^2 + (y-1)^2 = 1\), find the distance the two intersection points between a line that passes through the origin with angle \( \theta \) and the circle in terms of \( \theta \).

Hence calculate the distance if \( \theta = 60^\circ\).

Note: A previous version of this problem had \( \theta = 30^\circ\) which made the correct answer 1. Those who previously answered 1 have been given credit for a right answer.

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