Solve $\sin^{3}x+\cos^{3}x=1$ 
Solve for $x\\ \sin^{3}x+\cos^{3}x=1$

$\sin^{3}x+\cos^{3}x=1\\(\sin x+\cos x)(\sin^{2}x-\sin x\cdot\cos x+\cos^{2}x)=1\\(\sin x+\cos x)(1-\sin x\cdot\cos x)=1$
What should I do next?

Hint $$\sin^3(x)+\cos^3(x)=\sin^2(x)+\cos^2(x).$$
