If $ABC$ having vertices $A\left(a{\cos \theta }_1,a{\sin \theta }_1\right),B\left(a{\cos \theta }_{2}a{\sin \theta }_2\right),andC\left(a{\cos \theta }_3,a{\sin \theta }_3\right)$ is equilateral, then prove that ${\cos \theta }_1+{\cos \theta }_2+{\cos \theta }_3={\sin \theta }_1+{\sin \theta }_2+{\sin \theta }_3=0.$

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