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## Homework Statement

Express $$ 2 arctan (\sqrt\frac{a-b}{a+b} tan (\theta/2))$$ in terms of inverse cosine

## Homework Equations

I realise it amounts to find a smart substitution, but I can't find one.

## The Attempt at a Solution

I tried ##b/a=tan \theta## , but I can't find any way to get rid of the other tangent term. I would be really nice if the solution is not a direct substitution of the enormous formula for the inverse trig functions, as it only gets messy. Thanks in advance!!