If for some $\alpha, \beta ; \alpha \leq \beta, \alpha+\beta=8$ and $\sec ^2\left(\tan ^{-1} \alpha\right)+\operatorname{cosec}^2\left(\cot ^{-1} \beta\right)=36$, then $\alpha^2+\beta$ is __________

Let the inverse trigonometric functions take principal values. The number of real solutions of the equation $$2 \sin ^{-1} x+3 \cos ^{-1} x=\frac{2 \pi}{5}$$, is __________.

For $$n \in \mathrm{N}$$, if $$\cot ^{-1} 3+\cot ^{-1} 4+\cot ^{-1} 5+\cot ^{-1} n=\frac{\pi}{4}$$, then $$n$$ is equal to ________.

For $$x \in(-1,1]$$, the number of solutions of the equation $$\sin ^{-1} x=2 \tan ^{-1} x$$ is equal to __________.