Prove the identity \[\cos \theta - 2 \cos 3 \theta + \cos 5\theta = 2\sin \theta (\sin 2 \theta - \sin 4 \theta).\]

Solve the equations

\(\cos 2x = \sin x\),

\(3 \sec^2 x = \tan x + 5\)

giving in each case all solutions between \(0^\circ\) and \(360^\circ\).