How complex can it get

Algebra Level 4

if \( \dfrac{1}{a+w} + \dfrac{1}{b+w} +\dfrac{1}{c+w} +\dfrac{1}{d+w} =\dfrac{2}{w} \)

where \(w\) is the non real cube root of unity.

find the value of

\( \dfrac{1}{d+w^{2}} + \dfrac{1}{c+w^{2}} +\dfrac{1}{b+w^{2}} +\dfrac{1}{a+w^{2}} =?\)

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