Solution to Equation: Rearrange beta in terms of alpha

[richthegray]

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)))

 

[Georgepowell]

...i know its easy

I think it is quite difficult actually.

 

[qntty]

If tan-1 is supposed to be arctan or $\tan^{-1}$ then it doesn't appear to be possibly to solve it in terms of elementary functions.

Why do you need to solve it?