cos 3x

The answer at the back of the book says

2 sinē (1.5x) - 1

but how do you get that?

Isn't the "Double Angle Formula" for Cosine supposed to follow

cos 2Θ = 2 cosēΘ - 1 ??? Why does the answer say "sin"? And how do they know to use 1.5x? (the book is known to have many typos, if that helps...)