Tricky Inverse trigo problem

Question

$$[\arcsin(\arccos(\arcsin(\arctan (x) )))] =1$$

Where [*] represents the greatest integer function, and the task is to find the set of values of $x$ which satisfy the above equation.

I have no idea where to start from since there are so many inverse functions.

Answer 1

$$\lfloor\arcsin(\arccos(\arcsin(\arctan (x) )))\rfloor =1,$$ is equivalent to $$1\le\arcsin(\arccos(\arcsin(\arctan (x) )))<2.$$

Then taking the sine, which peaks at $1$,

$$\sin1\le\arccos(\arcsin(\arctan (x)))\le1.$$

Then taking the cosine, which is decreasing,

$$\cos1\le\arcsin(\arctan (x))\le\cos\sin1.$$

Then taking the sine, which is increasing,

$$\sin\cos1\le\arctan (x)\le\sin\cos\sin1.$$

Then taking the tangent, which is increasing,

$$\tan\sin\cos1\le x\le\tan\sin\cos\sin1.$$