（1+ sin^4θ）sinθ>(1+ cos^4θ) cosθ即sinθ+sin^5θ-cos^5θ-cosθ>0,也就是(sinθ-cosθ)+(sinθ-cosθ)(sin^4θ+sin^3θcosθ+sin^2θcos^2θ+sinθcos^3θ+cos^4θ)=(sinθ-cosθ)(1+sin^4θ+cos^4θ+sin^2θcos^2θ+sinθcosθ)=(sinθ-cosθ)(2+sinθcosθ-sin^2θcos^2θ)>0
对任意θ,(2+sinθcosθ-sin^2θcos^2θ)>0都成立,故只需sinθ-cosθ>0,而sinθ-cosθ=根号2分之一乘以sin(θ-pi/4),故θ属于（pi/4,5pi/4）.