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Geometry Level 3

\[\displaystyle\frac{\sin 1^\circ}{\sin 45^\circ \sin 46^\circ} + \frac{\sin 1^\circ}{\sin 47^\circ \sin 48^\circ} + \frac{\sin 1^\circ}{\sin 49^\circ \sin 50^\circ} + \cdots \\\displaystyle \cdots + \frac{\sin 1^\circ}{\sin 131^\circ \sin 132^\circ} + \frac{\sin 1^\circ}{\sin 133^\circ \sin 134^\circ} =\ ? \]


Source: 103 Trigonometry Problems, by Titu Andreescu.
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