如果sin^4 θ〖+sin〗^2 θcos^2 θ+cos

sin⁴θ + sin²θ cos²θ + cos⁴θ ≤ 3/4
4sin⁴θ + 4sin²θ cos²θ + 4cos⁴θ - 3 ≤ 0
4(sin⁴θ + cos⁴θ) + sin²2θ - 3 ≤ 0
4[ (sin²θ + cos²θ)² - 2sin²θ cos²θ ] + sin²2θ - 3 ≤ 0
4[ 1 - ½ sin²2θ ] + sin²2θ - 3 ≤ 0
1 - sin²2θ ≤ 0
cos² 2θ ≤ 0
⇒ cos 2θ = 0
2θ = π/2 , 3π/2 , 5π/2 , 7π/2 , 9π/2 , ...
θ = π/4 , 3π/4 , 5π/4 , 7π/4 (∵0 ≤ θ ≤ 2π)

sin^4 θ+sin^2 θ cos^2 θ+cos^4 θ
=(sin^2 θ+ cos^2 θ)^2-sin^2 θ cos^2 θ <=3/4

sin^2 θ cos^2 θ>=1/4
(2sin θ cos θ)^2>=1
sin 2θ =1 或 -1

與雨後晴空大的答案相同。