Cute cube roots

Algebra Level 4

i=110011ωi= ?\Large\color{#D61F06}{\sum_{i=1}^{1001}}\color{#3D99F6}{ \dfrac{1}{\omega^i}}= \ \color{#20A900}{?}

Given that ω\omega denotes a primitive cube root of unity, evaluate the above summation.

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