If $\frac{1}{2} \sin ^{-1}\left(\frac{3 \sin 2 \theta}{5+4 \cos 2 \theta}\right)=\tan ^{-1} x$, then $x=$

If $\operatorname{sech}^{-1} x=\log 2$ and $\operatorname{cosech}^{-1} y=-\log 3$, then $(x+y)=$

If $y=\tan ^{-1}\left(\frac{x}{1+2 x^2}\right)+\tan ^{-1}\left(\frac{x}{1+6 x^2}\right)$, then $\frac{d y}{d x}=$

The range of the real valued function $f(x)=\cos ^{-1}(-x)+\sin ^{-1}(-x)+\operatorname{cosec}^{-1}(x)$ is