Showing % Distribution within each Pie Chart Slice

So I have some data and I'm looking to present in an easy to understand, visual way.

The chart does a good job of explaining it but I want to show it visually via a pie chart but I am running into issues.

The chart is below shows that percentage among all 'Employee Types' -- this would be shown by the main pie chart, 3 slices with 72%, 2%, 27%.

Then I want to show within each of these three slices, the Y/N % in the next two columns.

I've been playing around with pie of pie and multiple other charts but I can't figure out what's the right way to do this. Let me know if you have any ideas.

I've also attached a poorly drawn paint image of what I am looking in the outcome.