A well-drawn graph is key to this question, as it shows you that for every instance of the cosine graph, the tangent graph only intersects it once. As the smallest positive root is denoted as alpha, the other roots within the stipulated range will just be periodic roots (i.e alpha + k(pi/2), where k is a constant) The period is pi/2 due to the given equation of the cosine graph.

Other notes:
A difficulty that may be faced will be the task of ruling out smaller possible roots, since we're sketching the graph w/o additional digital aid. The region of pi/8 < x < pi/4 may be foggy for some, since we don't know if there is actually an intersection there. Solve this issue by comparing y-values of the 2 trigo equations for the same critical x-value. Using pi/8, we see that the tan graph lies far away frm the cos graph, indicating that there is no possible intersect in that area.

Hope this helps