Question 157
The real numbers $a$, $b$ and $c$ are such that the polynomial $p(x) = x^{4} + a x^{3} + b x^{2} + a x + c$ 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 $y$, $0 \leq y \lt \pi$.