The number of integers for which the equation ${\sin }^{-1}x+{\cos }^{-1}x+{\tan }^{-1}x=n$ has real solution(s) is

Given equation is $\frac{\pi }{2}+{\tan }^{-1}x=n, \forall x\in [-1,1]$
Now LHS $\in \left[\frac{\pi }{4},\frac{3\pi }{4}\right]$
Integers in this interval are $1 \& 2$

Hence, there are $2$ integers for which the equation has real solutions