Solve, for $0<x\le \pi$, the equation

$$3{\sec }^{2}x-4\tan x=3$$

giving your answers, as appropriate, to 3 significant figures.

Show that

$$\frac{\sin 4\theta }{\sin 2\theta }-\frac{\cos 4\theta }{\cos 2\theta }\equiv 1$$

is false, and instead prove the identity:

$$\frac{\sin 4\theta }{\sin 2\theta }-\frac{\cos 4\theta }{\cos 2\theta }\equiv \frac{1}{\cos 2\theta }$$

Wait, correcting the identity format to match difficulty: Prove that

$$\frac{\sin 5\theta }{\sin \theta }-\frac{\cos 5\theta }{\cos \theta }\equiv \frac{\sin 4\theta }{\sin \theta \cos \theta }$$