Does there exist a function \(f (x)\) defined for all \(x \in \mathbb{R}\) and for all \(x, y \in \mathbb{R}\) satisfying the inequality \(| f (x + y) + \sin x + \sin y | < 2\)?
Solve the equation: \(|x-2005| + |2005-x|=2006\).
Solve the inequality: \(|x + 2000| <|x - 2001|\).