if`omegaa n domega^2` are the nonreal cube roots of unity and `[1//(a+omega)]+[1//(b+omega)]+[1//(c+omega)]=2omega^2` and `[1//(a+omega)^2]+[1//(b+omega)^2]+[1//(c+omega)^2]=2omega^` , then find the value of `[1//(a+1)]+[1//(b+1)]+[1//(c+1)]dot`

Explanation

To solve the problem, we need to analyze the given equations and use the properties of cube roots of unity. Let's break it down step by step.

### Step 1: Understanding the Cube Roots of Unity
The non-real cube roots of unity are given by:
- \( \omega = e^{2\pi i / 3} = -\frac{1}{2} + i\frac{\sqrt{3}}{2} \)
- \( \omega^2 = e^{-2\pi i / 3} = -\frac{1}{2} - i\frac{\sqrt{3}}{2} \)

These satisfy the equation:
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