If $\left|\sin x-\cos ^2 x\right| \geq\left|3-3 \sin x+\sin ^2 x\right|+4|\sin x-1|$, then $x=$

The number of real roots of the equation $\sin \left[2 \cos ^{-1}\left\{\cot \left(2 \tan ^{-1} x\right)\right\}\right]=0$ that are greater than or equal to one are

If $\operatorname{sech}^{-1}(1 / 2)-\operatorname{cosech}^{-1}(3 / 4)=\log _e k$, then

The perimeter of a $\triangle A B C$ is 6 times the arithmetic mean of the sine of its angles. If its side $B C$ is of unit length, then $\angle A=$