$$ \text { If } \frac{\cos ^2 48^{\circ}-\sin ^2 12^{\circ}}{\sin ^2 24^{\circ}-\sin ^2 6^{\circ}}=\frac{\alpha+\beta \sqrt{5}}{2} \text {, where } \alpha, \beta \in \mathbb{N} \text {, then } \alpha+\beta \text { is equal to ___________} $$

The value of $$\tan 9^{\circ}-\tan 27^{\circ}-\tan 63^{\circ}+\tan 81^{\circ}$$ is __________.

If $${\sin ^2}(10^\circ )\sin (20^\circ )\sin (40^\circ )\sin (50^\circ )\sin (70^\circ ) = \alpha - {1 \over {16}}\sin (10^\circ )$$, then $$16 + {\alpha ^{ - 1}}$$ is equal to __________.