Let
$
\alpha=\frac{1}{\sin 60^{\circ} \sin 61^{\circ}}+\frac{1}{\sin 62^{\circ} \sin 63^{\circ}}+\cdots+\frac{1}{\sin 118^{\circ} \sin 119^{\circ}}
$
Then the value of $\left(\frac{\operatorname{cosec} 1^{\circ}}{\alpha}\right)^2$
is $\_\_\_\_$
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