Trigonometric Multiplication

I'm working through a complex number question and need to do a certain multiplication that for some reason I just can't get to equal what it needs to be.

The multiplication is as follows:

(cos^2(3θ) + jsin^2(3θ)) x (cos3θ + jsin3θ)

Could anyone please have a go and see what they get because I am not very familiar with the rules of multiplication when it comes to trig functions.