A geometry problem by Mohammed Siraj

Geometry Level pending

The following image contains 4 congruent circles that are tangent to one another and line AZB. Line segment BC is parallel to the horizontal, angle ABC is 45 degrees, and the measure of line segment AZ is 2((2^0.5)-1). If the point Z touches the right bottom circle at only one point, what is the area of the pink region? Leave your answer in terms of pi.

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