For 0° < θ < 90°, which statement comparing si$n^4$θ + co$s^4$θ with si$n^6$θ + co$s^6$θ is true?

With $p$ = sinθ·cosθ the two expressions are $1-2p^2$ and $1-3p^2$. On 0° < θ < 90° the product $p$ is never zero, so $3p^2>2p^2$ and therefore $1-2p^2>1-3p^2$. Check at θ = 30°: 0.625 against 0.4375, and at θ = 10°: 0.9415 against 0.9123. The two would be equal only at $p=0$, which needs θ = 0° or 90° — both excluded — so the comparison never flips.