The diagram shows part of the curve \(y = 8 - \sqrt{4 - x}\) and the tangent to the curve at \(P(3, 7)\).

(i) Find expressions for \(\frac{dy}{dx}\) and \(\int y \, dx\).

(ii) Find the equation of the tangent to the curve at \(P\) in the form \(y = mx + c\).

(iii) Find, showing all necessary working, the area of the shaded region.