(ITA - 2024)Sabendo que e para, calculee

(ITA - 2024)

Sabendo que \(tan(\alpha +\beta ) = -2\) e \(sen(\alpha ) = (4-\sqrt{5})sen(\beta )\) para\(\alpha,\beta \ \epsilon \ (0,\pi/2)\), calcule

\(tan\left ( \frac{\alpha +\beta }{2} \right ), tan \left ( \frac{\alpha -\beta }{2} \right )\) e \(\frac{tan\left ( \frac{\alpha -\beta }{2} \right )}{ tan \left ( \frac{\alpha +\beta }{2} \right )}\)