Solve `sin^(-1)x+sin^(-1)2x=pi/3dot`

Explanation

`sin^(-1) x + sin^(-1) 2x = (pi)/(3)`(i)
or `sin^(-1) 2x = sin^(-1).(sqrt3)/(2) - sin^(-1) x`
`= sin^(-1) [(sqrt3)/(2) sqrt(1 - x^(2)) - x sqrt(1 - (3)/(4))]`
or `2x = (sqrt3)/(2) sqrt(1 -x^(2)) - (x)/(2)`
or `((5x)/(2))^(2) = (3)/(4) (1 -x^(2))`
or `28x^(2) = 3`
or `x = sqrt((3)/(28)) = (1)/(2) sqrt((3)/(7))`
{ `:' x = -(1)/(2) sqrt((3)/(7))` makes L.H.S. of Eq. (i) negative)