The equation of the sphere (S) is given as x² + y² + z² - 2x - 2y - 2z - 1 = 0.

Step 1: Analyze the sphere equation.
The equation of the sphere $(S)$ is given as $x^2 + y^2 + z^2 - 2x - 2y - 2z - 1 = 0$.
To find the center and radius, we complete the square for each variable:

$$(x^2 - 2x) + (y^2 - 2y) + (z^2 - 2z) = 1$$

Add $(1)^2$ to complete the square for each term:

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