Tax on Grand Total

Is there any way I can calculate tax on a cart’s grand total?

This is how the tax is currently calculated:
Product Tax + Shipping Tax = Total Tax

How the client would like the tax to be calculated:
Products + Shipping = Cart Total
Total Tax = Cart Total + 15%

What makes this a little more challenging for me, is that products are listed inclusive of tax. If it would make things easier, I could ask the client if we could enter prices excluding tax.

Any help would be very much appreciated.

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