Syncing Timeline From-To Dates With Cells

I have a pivot table that is linked to a timeline widget, allowing the user to manipulate the table based on their date range selection. I've also allowed the user to manually type in a a 'Date From' and 'Date To' value, and this refreshes the pivot table whenever there's a change. This works as far as the table updating goes, but it does not synchronise with the timeline.

So…I need a solution whereby the date range in the timeline always matches the date range in the cells — and vice-versa.

I've attached a workbook to demonstrate what I mean.