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Simplify (3sin2alpha)/(5+3cos2alpha)+tan...

Simplify `(3sin2alpha)/(5+3cos2alpha)+tan^(-1)(tan(alpha/4))`,where -`pi/2 lt alpha lt pi/2`

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`tan^(-1)[(3sin2alpha)/(5+3cos2alpha)]+tan^(-1)[tanalpha/4]`
`tan^(-1)[(6tanalpha)/(8+2tan^2alpha)]+tan^(-1)(tanalpha/4)`
`(6tan^2alpha)/(4(8+2tan^2alpha))<1`
`tan^(-1)[((3tanalpha)/(4ttan^2alpha)+tanalpha/4)/(1-(3tanalpha)/(4+tan^2alpha)*tanalpha/4)]`
`tan^(-1)((12tanalpha+4tanalpha+tan^3alpha)/(16+tan^2alpha))`
`tan^(-1)((16tanalpha+tan^3alpha)/(16+tan^2alpha))`
`tan^(-1)((tanalpha(16+tan^2alpha))/(16tan^2alpha))`
`tan^(-1)tanalpha=alpha`.
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