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**Kurama** There is this problem:

If $\displaystyle tan{x}={a}{\tan{\frac{x}{3}}}$, express $\displaystyle \tan{\frac{x}{3}}$ in terms of *a*.

I expressed tan in terms of $\displaystyle \tan{\frac{x}{3}}$ and isolated it. I obtained $\displaystyle \tan{\frac{x}{3}}=\pm{\sqrt{{\frac{3-a}{1-3a}}}}$.

But what about the sign? For example, for the first period $\displaystyle \tan{\frac{x}{3}}$ should be positive for values of x greater than 0 and negative for values of x less than 0, but there does not seem to be anything in the expression I obtained that can account for the sign. Could somebody tell me what I have done wrong?

Thanks a lot.