In `DeltaABC`, prove that:
`sin^(2)A+sin^(2)B+sin^(2)C` `=2+2cosAcosBcosC.`

Explanation

To prove the identity \( \sin^2 A + \sin^2 B + \sin^2 C = 2 + 2 \cos A \cos B \cos C \) in triangle \( \Delta ABC \), we will follow these steps:

### Step 1: Use the identity for sine squared
We know the identity:
\[ \sin^2 x = \frac{1 - \cos(2x)}{2} \]
Using this, we can express \( \sin^2 A \), \( \sin^2 B \), and \( \sin^2 C \):
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