Solution to Equation

I have been struggling with the solution to the following equation, i know its easy but just cannot solve it. I need to rearrange it to have alpha in terms of beta.

beta = alpha+ tan-1(0.5(tan(alpha )))
 
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If tan-1 is supposed to be arctan or [itex]\tan^{-1}[/itex] then it doesn't appear to be possibly to solve it in terms of elementary functions.

Why do you need to solve it?
 

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