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Proving that $ \frac{1}{\sin(45°)\sin(46°)}+\frac{1}{\sin(47°)\sin(48°)}+...+\frac{1}{\sin(133°)\sin(134°)}=\frac{1}{\sin(1°)}$

Find the smallest postive integer n such that :

$\dfrac{1}{\sin 45^\circ \sin 46^\circ} + \dfrac1{\sin 47^\circ \sin 48^\circ} + \dots + \dfrac1{\sin 133^\circ \sin 134^\circ} = \dfrac1{\sin n^\circ}$

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    The same question (with the $n=1^\circ$ answer) appeared in december 2011 [here](http://math.stackexchange.com/questions/95291/proving-that-frac1-sin45-sin46-frac1-sin47-sin48-fr).2012-11-13

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