KöMaL 2012 A556

Prove that for arbitrary real numbers $a_1,\ldots,a_n$ there exist a real $t$ such that $\sum_{i=1}^n \big|\sin(t-a_i)\big| \le \ctg\frac\pi{2n}.$

Official text KöMaL. 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.