TxO Math Bowl 2024 - Team Contest - Problem 26

The bottom layer of a number pyramid is constructed using the numbers

\sin^2(90^\circ), \sin^2(89^\circ), \sin^2(88^\circ) \dots \sin^2(0^\circ)

in that order. Each subsequent row above is constructed by taking the absolute value of the difference of adjacent elements in the previous row. Find the value at the top of the pyramid.