algebra precalculus - An identity relating the roots of $F(x)=x^3+x^2+4x+4$

Demonstrate how
$$\frac1{x_1} + \frac1{x_2} + \frac1{x_3} + \frac1{x_1x_2} + \frac1{x_2x_3} + \frac1{x_3x_1} = -\frac34$$
where $x_1, x_2, x_3$ are roots of the polynomial $F(x) = x^3 + x^2 + 4x + 4$.

Can someone help me please, thank you!