A thin hoop of radius \(R\) lies in the \(xy\)-plane with its center at the origin. The linear mass density \(\lambda\) of the hoop varies with angular position \(\theta\) measured from the positive \(x\)-axis according to \(\lambda(\theta) = \lambda_0 (1 + \cos^2\theta)\), where \(\lambda_0\) is a positive constant. Which of the following expressions represents the rotational inertia of the hoop about a central axis perpendicular to the plane of the hoop?