Determining the general form of $10^x \bmod 210$

Determining the general form of $10^x \bmod 210$

While solving a problem I came across solving $10^x\bmod 210$ for various
values of $x$. It seems that the values repeat after an interval of 6 for
$x\geq4$. Can any one explain how can solve this equation for some value
of $x$ and show that it repeats at an interval of 6. Note that $210 =
2\times3\times5\times7$ is a product of the first four primes.
Thanks