`(1)/(a + omega) + (1)/(b+omega) +(1)/(c + omega) + (1)/(d + omega) =(1)/(omega)` where, a,b,c,d, `in` R and `omega` is a complex cube root of unity then find the value of `sum (1)/(a^(2)-a+1)`

Explanation

To solve the equation

\[ \frac{1}{a + \omega} + \frac{1}{b + \omega} + \frac{1}{c + \omega} + \frac{1}{d + \omega} = \frac{1}{\omega} \]

where \( a, b, c, d \in \mathbb{R} \) and \( \omega \) is a complex cube root of unity, we will follow these steps:

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