Suppose that we have a equation of third degree as follows:

$$
x^3-3x+1=0
$$

Let $a, b, c$ be the roots of the above equation, such that $a < b < c$ holds. How can we find the answer of the following expression, without solving the original equation?

$$
\frac {a}{b} + \frac {b}{c} + \frac {c}{a}
$$