How do we solve $\sin(\sin(x))=a$? While I was solving a sum, I got stuck at how to go further when I incurred
$\sin(\sin(x^2))=1$ or $0$, where $x\in \mathbb{R}$.
Can someone help me to proceed this step and also a general way of approaching $\sin(\sin(x))$ type problems?
Hint:

You can invert a relation like $$v=\sin(u)$$ with $$u=\arcsin(v)+2k\pi\lor u=\pi-\arcsin(v)+2k\pi.$$

Use the trick once to get $\sin(x^2)$ and a second time to get $x^2$.



Notice that the value of the sine is limited to the range $[-1,1]$, and as it is monotonous there, 

$$\sin(\sin(t))\in[-\sin(1),\sin(1)]$$ and there are no solutions for $a$ outside this range. ($\sin(1)\approx0.841471$)
draw graphs of sin(x) and arcsin(a).
the solution will be the intersection point of these two graphs.