E is a point in the square ABCD, and the angle ade is equal to the angle DAE is equal to 15 degrees. It is proved that BCE is an equilateral triangle

The side length of the square is a
Sine theorem in triangle ade
AD/sin∠AED=AE/sin∠ADE
sin∠AED=1/2
AE=2a*sin15°
Inner cosine theorem of triangle AEB
BE^2=AB^2+AE^2-2AB*AE*cos∠EAB=a^2+4a^2*sin15*sin15-4a^2*sin15*cos75
BE^2=a^2 BE=a
Similarly, CE = a

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