I'm teaching numerical analysis with Maple and then I started with fixed iteration method.
When I programed the method which is simple, I got the solution as:
f := x->2*tan(x)-x-1;
g := x->arctan((1/2)*x+1/2); # fixed point method where the solution of x=g(x) is the the solution f(x)=0
x := 0.2; for k from 0 to 20 do x[k+1] := evalf(g(x[k])) end do; this line give the solution