Problem involving Power-Reducing Formula

[DinosaurEgg]

Homework Statement

Homework Equations

How in the world did they get their solution? Where did 27/8 come from?

The Attempt at a Solution

I did the arithmetic with the fractions inside before distributing the 9, and ended up getting something like -9/4 cos2x + 9/4 cos4x. Completely different from theirs.

 

[Bohrok]

In the step above that, you have 1/4 + 1/8 = 2/8 + 1/8 = 3/8, then times 9 is 27/8