How can I express cos(4θ) in terms of cos(2θ)? (Pointers on trigonometric algebraic manipulation welcome)

Let theta = x for typing purposes here.
We will the formula of because (2x) = 2 ( because x)^2 - 1cos (4x) = because [2 * (2x)]. Let 2x = y.
Now using the formula

because (2y) = 2 ( because y)^2 - 1 = 2 [because (2x)]^2 - 1

Therefore
because (2y) = because (4x) = 2 [because (2x)]^2 - 1