Express cos4θ and sin4θ in terms of sines and cosines of multiples of θ. Using a trignometric identity: cos (2θ) = cos^2(θ) - sin^2(θ) Since 4θ = 2*2θ, so we have: cos(4θ) = cos^2(2θ) - sin^2(2θ) Using another trignometric identity, we have: sin(2θ) = 2 sin(θ) cos(θ) Since 4θ = 2*2θ, so we have: sin(4θ) = 2 sin(2θ) cos(2θ)