ILL 1967 Problem 55

Find all $x$ for which, for all $n,$ $\sum^n_{k=1} \sin {k x} \leq \frac{\sqrt{3}}{2}.$

Dataset text AoPS wiki problems. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.