Trigonometric Functions And Equations

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 _____________.