Show that the equation

$$3\cos \theta -2=5\sin \theta \tan \theta$$

can be written in the form

$$8{\cos }^2\theta -2\cos \theta -5=0$$

Hence solve, for $0\le x<\pi$,

$$3\cos 2x-2=5\sin 2x\tan 2x$$

giving your answers, where appropriate, to 2 decimal places.