MathNet 1992 — Part 01 Question 61

Let $f(x) = a\cos(x + 1) + b\cos(x + 2) + c\cos(x + 3)$, where $a$, $b$, $c$ are real. Given that $f(x)$ has at least two zeros in the interval $(0,\pi)$, find all its real zeros.