If the tangent to the curve $y = x + \sin y$ at a point $(a, b)$ is parallel to the line joining $\left(0, \frac{3}{2}\right)$ and $\left(\frac{1}{2}, 2\right)$, then\\
(1) $b = a$\\
(2) $|b - a| = 1$\\
(3) $|a + b| = 1$\\
(4) $b = \frac{\pi}{2} + a$