Prove that the equation `2s in x|x|+a` has not solution for `a in ((3sqrt(3)-pi)/3-oo)dot`

Explanation

We have
`2 sin x=|x|+a`.
Consider graphs of `y=2 sin x` and `y=|x|`.

Equation `2 sin x=|x|+a` will have a solution so long as the line `y=|x|+a` intersects or at least touches the curve, `y=2 sin x`. In this case, we must have
`dy//dx=2 cos x=1=` Slope of the line
`rArr x=pi//3`.
Hence, the solution does not exist if `pi/3+a gt 2 "sin" pi/3`
`rArr a gt (3sqrt(3)-pi)/3`