Yet again another hard question I don't know how to do!

Prove that 1+ cos 2θ+ cos 4θ+ cos 6θ= 4 cosθcos 2θcos 3θ

Hence, find all the angles between 0 degrees and 180 degrees inclusive, which satisfy the equation(below)

cos 2θ+ cos 4θ+ cos 6θ= -1

Thank you all in advance