If \sqrt{2 + \sqrt{2 + \sqrt{2 + ...}}} = \operatorname{cosec} \theta, then what is \sin \theta equal to?

Explanation

Let x = \sqrt{2 + \sqrt{2 + ...}}. Then x = \sqrt{2 + x} \Rightarrow x^2 - x - 2 = 0. The positive root is x = 2. Thus, \operatorname{cosec} \theta = 2, which means \sin \theta = \frac{1}{2}.

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