Question 152
Let $a$, $b$ and $c$ be real numbers such that $p(x) = x^4 + a x^3 + b x^2 + a x + c$ has exactly three different real roots; these roots are $\tan y$, $\tan 2y$ and $\tan 3y$ for some real number $y$. Find all possible values of $y$, $0 \le y \lt \pi$.