9. $$\mathrm { f } ( x ) = 2 x ^ { \frac { 1 } { 3 } } + x ^ { - \frac { 2 } { 3 } } \quad x > 0$$ The finite region bounded by the curve \(y = \mathrm { f } ( x )\), the line \(x = \frac { 1 } { 8 }\), the \(x\)-axis and the line \(x = 8\) is rotated through \(\theta\) radians about the \(x\)-axis to form a solid of revolution. Given that the volume of the solid formed is \(\frac { 461 } { 2 }\) units cubed, use algebraic integration to find the angle \(\theta\) through which the region is rotated.