The value of $$\sin ^{-1}\left\{\cot \left(\sin ^{-1} \sqrt{\frac{2-\sqrt{3}}{4}}+\cos ^{-1} \frac{\sqrt{12}}{4}+\sec ^{-1} \sqrt{2}\right)\right\}$$ is

The sum of the infinite terms of the series $\cot ^{-1}\left(1^2+\frac{3}{4}\right)+\cot ^{-1}\left(2^2+\frac{3}{4}\right)$ $+\cot ^{-1}\left(3^2+\frac{3}{4}\right)+\ldots$ is equal to

If $$\left(\sin ^{-1} x\right)^2-\left(\cos ^{-1} x\right)^2=a \pi^2$$, then the range of $$a$$ is

The equation $$3 \cos ^{-1} x-\pi x-\pi / 2=0$$ has