cos(th)*sin(th)==f is equivalent to th==arcsin(2*f), and so substitution eq.subs({th:arcsin(2*f)}) should do the job.
cos(th)*sin(th)==f is equivalent to th==arcsin(2*f)th==arcsin(2*f)/2, and so substitution eq.subs({th:arcsin(2*f)})eq.subs({th:arcsin(2*f)/2}) should do the job.