The value of $$\sin \left(2 \sin ^{-1} 0.8\right)$$ is equal to

The principal value of $$\sin ^{-1}\left(\sin \left(\frac{2 \pi}{3}\right)\right)$$ is

If $$2 \tan ^{-1}(\cos x)=\tan ^{-1}(2 \operatorname{cosec} x)$$, then the value of $$x$$ is

If $$y=\tan ^{-1}\left[\frac{1}{1+x+x^2}\right]+\tan ^{-1}\left[\frac{1}{x^2+3 x+3}\right], x>0$$, then $$\frac{d y}{d x}=$$