If $\sin ^2\left(10^{\circ}\right) \sin \left(20^{\circ}\right) \sin \left(40^{\circ}\right) \sin \left(50^{\circ}\right) \sin \left(70^{\circ}\right)=\alpha-\frac{1}{16} \sin \left(10^{\circ}\right)$, then $16+\alpha^{-1}$ is equal to $\_\_\_\_$
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