We have `cos^(-1)(cos x)=[x]`
To find the roods of the equation, we draw the graphs of `y=cos^(-1)(cos x)" and "y = [x]` and then find the points of intersection.
From the graph, roots are 0, 1, 2, 3, and the value ot x for which `3=2pi-x or x= 2 pi-3`. Hence the sum of roots is `2pi+3`