Tough Moment of Inertia Problem About a Super Thin Spherical Shell Using Spherical Coordinates

I need to compute the moment of inertia of a spherical shell with radius $$R$$, constant density $$\rho$$, and total mass $$M$$ throughout some (any) axis through the origin.

The question specifies that this should be a double integral, since it's a super thin shell. So that means I'd need to use $$dA = R^2\sin{\phi}d{\phi}d{\theta}$$.

From here, though, I'm stuck, and even unsure where to start. Any help would be much appreciated.

The mass of the $$dA$$ area is $$dm=\rho dA=\frac{M}{4\pi R^2}dA$$. I assumed here that $$\rho$$ is a surface density. You can calculate the moment of inertia with respect to any axis, they are all equal. Then for simplicity, use the axis where $$\phi=0$$. The distance from this axis is $$r=R\sin\phi$$, so $$I=\iint r^2dm=\int_0^{2\pi} d\theta\int_0^\pi\frac{M}{4\pi R^2}R^4\sin^3\phi$$