(a) Given that \(2\cos x=3\tan x\), show that

\(2\sin^2x+3\sin x-2=0.\)

(b) Hence solve

\(2\cos\left(2\alpha+\frac{\pi}{4}\right) =3\tan\left(2\alpha+\frac{\pi}{4}\right)\)

for \(0\lt \alpha\lt \pi\) radians, giving your answers in terms of \(\pi\).