Let \( B \) and \( C \) be the two points on the line \( y + x = 0 \) such that \( B \) and \( C \) are symmetric with respect to the origin. Suppose \( A \) is a point on \( y - 2x = 2 \) such that \( \triangle ABC \) is an equilateral triangle. Then, the area of the \( \triangle ABC \) is:
