Problem - 3899
Let $\theta\in[0, 2\pi]$ satisfying $$\cos^5\theta -\sin^5\theta < 7(\sin^3\theta -\cos^3\theta)$$
Find the range of $\theta$.
The given relation is equivalent to
$$\cos^5\theta +7\cos^3\theta < \sin^5\theta + 7\sin^3\theta$$
Because the function $$f(x)=x^5 + 7x^3$$ monotonically increases, therefore we must have $$\cos\theta < \sin\theta \implies \theta\in\boxed{\Big(\frac{\pi}{4},\frac{5\pi}{4}\Big)}$$