Step-By-Step Half Angle Identities

Question

I can't really find an answer for this anywhere. Could I get a Step-By-Step solution for the following problem?

Find cos theta/2 if cos theta=4/5 and 270 degrees< theta<360 degrees

Answer 1

cos (θ/2) = ±√[(1 + cos θ) / 2]

cos (θ/2) = ±√[(1 + (4/5) / 2]

cos (θ/2) = ±√[(9/5) / 2]

cos (θ/2) = ±√[9/10]

cos (θ/2) = ±(3√10) / 10]

Determine in which Quadrant the half angle is to select positive or negative.

Answer 2

One of the cosine double angle formulas is:

cos(2θ) = 2(cosθ)² - 1

Can you use that to figure out the answer? Note that we can use θ/2 and θ instead θ and 2θ and that might make the solution more apparent.