Your method, finding the zeros of the function , is as good as any. Notice that these are all simple zeros (no repeated roots), so the graph of f(x) will cross the axis at each of these zeros. Therefore it will be alternately positive and negative in the intervals (0,π/3), (π/3,π), (π,5π/3) and (5π/3,2π). All you need to do is to check that f(x) is positive in the first of those intervals.