The diagram shows parts of the curves \(y = (4x + 1)^{\frac{1}{2}}\) and \(y = \frac{1}{2}x^2 + 1\) intersecting at points \(P(0, 1)\) and \(Q(2, 3)\). The angle between the tangents to the two curves at \(Q\) is \(\alpha\).

(i) Find \(\alpha\), giving your answer in degrees correct to 3 significant figures.

(ii) Find by integration the area of the shaded region.