# Trig sum

**Algebra**Level pending

If a geometric progression has \(a_{1}=2.tg (\frac{\pi}{5})\) as its first term and \(q=tg^{2} (\frac{\pi}{5})\) as its ratio of progression, the sum of all its terms, for \(n\) terms, with \(n\) varying from \(1\) to \(\infty\), can be expressed as \(\zeta=tg (\frac{s.\pi}{r})\), such that \(s\) and \(r\) are coprime positive integers. So, what's \(s+r\)?

**Details and assumptions**

You might desconsider answers out of the interval \([0,\frac{\pi}{2}]\)