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