Sir Mike Ambrose is the author of the question.
Let the radius of one of the two equal circles be 1 unit.
Total shaded area ÷ Rectangle area will be;
(½(2x4)-π-(1-¼(4-π)-((180-2tan–¹(0.5))π÷360)+(0.5sin(180-2tan–¹(0.5)))))÷(2x4)
= (4-π-(¼(π)-((180-2tan–¹(0.5))π÷360)+(0.5sin(180-2tan–¹(0.5)))))÷8
= (4-π-0.0782494456)÷8
= 0.78015790081÷8
= 0.0975197376
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