KöMaL 2010 B4246

Given that the roots $x_1$, $x_2$, $x_3$ of the equation $x^3$-($a$+2)$x^2$+(2$a$+1)$x$-$a$=0 satisfy $\frac{2}{x_1} + \frac{2}{x_2} = \frac{3}{x_3}$, solve the equation.