Let \( a \) be the length of a side of a square \( OABC \) with \( O \) being the origin. Its side \( OA \) makes an acute angle \( \alpha \) with the positive \( x \)-axis and the equations of its diagonals are \( (\sqrt{3}+1)x + (\sqrt{3}-1)y = 0 \) and \( (\sqrt{3}-1)x - (\sqrt{3}+1)y + 8\sqrt{3} = 0 \). Then \( a^{2} \) is equal to:
