$sin^{-1}(]sin(x)-varepsilon,sin(x)+varepsilon[)$=?

As in the title:
$$
sin^{-1}(]sin(x)-varepsilon,sin(x)+varepsilon[)=
{yin mathbb{R}, sin(y)in ]sin(x)-varepsilon,sin(x)+varepsilon[}$$

can I say that $Arcsin(sin(x)-varepsilon)<y<Arcsin(sin(x)+varepsilon)$ ?

But how to continue ?

Thank you