A regular 30-gon

Geometry Level 5

If \(A_1 , A_2 , A_3 , \ldots , A_{30}\) are the vertices of a regular 30-gon inscribed in a unit circle, then find

\[{|A_1 A_2|}^2 + {|A_1 A_3|}^2 + {|A_1 A_4|}^2 + \cdots + {|A_1 A_{30}|}^2 .\]

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