Let the set of all a ∈ R such that the equation cos 2 x + a sin x=2 a -7 has a solution be [ p, q ] and r = tan 9^°- tan 27^°-1/(cot 63^°)+ tan 81^°,…

Let the set of all $\displaystyle \mathrm{a} \in \mathrm{R}$ such that the equation $\displaystyle \cos 2 \mathrm{x}+\mathrm{a} \sin x=2 \mathrm{a}-7$ has a solution be $\displaystyle [\mathrm{p}, \mathrm{q}]$ and $\displaystyle \mathrm{r}=\tan 9^{\circ}-\tan 27^{\circ}-\frac{1}{\cot 63^{\circ}}+\tan 81^{\circ}$, then pqr is equal to $\displaystyle \_\_\_\_$.