OME 2019 Problem 3

The real numbers $a$ , $b$ and $c$ verify that the polynomial $p(x)=x^4+ax^3+bx^2+ax+c$ has exactly three distinct real roots; these roots are equal to $\tan y$ , $\tan 2y$ and $\tan 3y$ , for some real number $y$ . Find all possible values of $y$ , $0\leq y < \pi$ .