Use the Pythagorean Trig Identity, sin^2θ+cos^2θ=1, to prove that sin^4θ-cos^4θ=1-2cos^2θ.

With the advice of my teacher, I started by making a chart. One side is "sin^4θ - cos^4θ", and the other is "1 - 2cos^2θ". He said I'm not supposed to plug in any numerical values, but I'm not sure what to do next.