The curves \(C_1\) and \(C_2\) have equations \(x^2 + y^2 = 4\) and \(y^2 = \frac{4}{1+x^2}\) respectively.
Find the exact coordinates of the points of intersection of \(C_1\) and \(C_2\).[2]
Find the area of the shaded region, giving your answer correct to \(3\) decimal places.[2]
Find the exact volume of the solid obtained when the shaded region is rotated through \(\pi\) radians about the \(x\)-axis.[3]