We meet at infinity

Geometry Level 3

\(1)\) First we have a square with side \(\sin { \xi } \).

\(2\) Then we join the midpoints of square to get another square.And this process continues forever.Means we join midpoints of squares and get new squares.

Sum of areas of all these square is equal to \(\frac { 3 }{ 2 } \).Then \(\xi =?\)

Details and assumptions:-

\(1)\)\(0°<\xi <90°\) and \(\xi\) is in degrees.

This problem is original.

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