Solve `sin^(-1) (sin 6x) = x, x in [0,pi]`

Explanation

`sin^(-1) (sin 6x) = x`
`rArr sin 6 x = sin x`
`rArr sin 6 x - sin x = 0`
`rArr 2 sin.(5x)/(2) cos.(7x)/(2) = 0`
`rArr (5x)/(2) n pi " or " (7x)/(2) = (2n + 1) (pi)/(2), n in Z`
`rArr x = (2n pi)/(5) " or " x = (2n + 1) (pi)/(7)`
`rArr x = (pi)/(7) , (3pi)/(7), (5pi)/(7), pi, 0, (2pi)/(5), (4pi)/(5)`
But `x = (5 pi)/(7), pi, (4pi)/(5)` are not possible as any solution `[-(pi)/(2), (pi)/(2)]`