Conservation of angular momentum for a nonrigid body

Question:

The sun is not a rigid body but a hot ball of gas. The period of rotation varies from 37 days at the pole to 26 days at the equator. The mean radius of the sun is $7\times 10^8\text{ m}$. Suppose the sun collapses into a neutron star of radius approximately $10^4\text{ m}$. Assume that the neutron star is a spherical ball. Estimate the final period of rotation of the neutron star. You may assume it is a rigid sphere for this approximate calculation.

So I understand how this is a conservation of angular momentum problem and the neutron star side is just $I\omega$ where $I$ is for a solid sphere, but I don't know what to do about the sun side. It seems like it would be an integral of all the disks of the sphere for $I\omega$, but it doesn't say anywhere about whether or not density is uniform throughout the sun and how $\omega$ varies (linearly, by curve of the sphere?). It seems like density should be uniform, so I could probably figure out the I using that. Then I thought I could use the average value of $\omega$ and just multiply it with the integral for $I$, but I can't do this since I don't know the function for $\omega$ so I wouldn't be able to integrate it along the interval and then divide by the interval. Can anyone help me with this? Thanks!

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