Solution to Equation: Rearrange beta in terms of alpha

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The equation beta = alpha + tan-1(0.5(tan(alpha))) presents challenges in rearranging to express alpha in terms of beta. Some participants believe that solving for alpha in this context is not feasible using elementary functions. The discussion highlights the complexity of the equation and questions the necessity of finding a solution. Overall, the difficulty in rearranging the equation is a central concern among participants. The conversation emphasizes the limitations of traditional algebraic methods in this case.
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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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...i know its easy

I think it is quite difficult actually.
 
Last edited:
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?
 

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