Having trouble applying half angle formula in this question,

Any hints would be great

sin^4Θ=3/8 - 1/2cos(2Θ) + 1/8 cos(4Θ) is a solution for any angle Θ

use half angle formula and cos^2(2Θ)=1/2 cos(4Θ) +1/2

thanks

p.s just moved this, posted it in geometry by accident