Prove that there is a $\theta\in (13\pi/6, 7\pi/2 )$ such that
$$\tan(2\theta - 5\pi)\tan(3\theta + 4\pi) = 2/3.$$
I started by defining a function on $\mathbb R$ such that $f(x) = \cos 3x\sin 2x$ hoping to end up with something but I'm really stuck as I have to prove that it is continuous on that given range etc.
Is there anyone who has a different approach than that ?