How can I proof or demonstrate mathematically that solid angle integral from a point outside a closed surface is zero?

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I would like to know how can I proof or demonstrate mathematically that solid angle integral from a point outside a closed surface is zero. How can this be done?

I have already demonstrated the value of $4\pi$ for a point inside. In this case, I used a double integral in spherical coordinates over a spherical element, with polar angle from zero to $2\pi$ and azimuthal angle from zero to $1\pi$. Like, as we use to determine the sphere total area.

Thanks