Given: \(a\ne b\ne c\) and \(\left(b-c\right)\sqrt[3]{1-a^3}+\left(c-a\right)\sqrt[3]{1-b^3}+\left(a-b\right)\sqrt[3]{1-c^3}=0\)

Prove: \(\left(1-a^3\right)\left(1-b^3\right)\left(1-c^3\right)=\left(1-abc\right)^3\)

Do not use trigonometric formulas. Prove: Cos \(72^0\)x Cos \(36^0=\dfrac{1}{4}\)