Common zeros of sin(nx) on [0, 2π]

Consider the 10 functions, all with domain $[0, 2\pi]$ and defined as $f_n(x) = \sin(nx)$, where $n$ is an integer with $1 \le n \le 10$.

$f_1(x) = \sin(x),\ f_2(x) = \sin(2x),\ f_3(x) = \sin(3x),\ \dots,\ f_{10}(x) = \sin(10x)$

How many values of $x \in [0, 2\pi]$ exist such that $f_n(x) = 0$ for all integers $n$ with $1 \le n \le 10$?