Solve for A: cos 9A = (cos 15A)(cos 8A)
Now use on each side:
So that, at least, gives some solutions:
But what happens next with the remaining expression, I'm not sure. You could use and then remove the factor from both sides to get:
(which doesn't give any more answers that we haven't already got from ), or:
which you could then express simply in terms of , but it would be pretty horrendous!