<Qua-2024-739>, hint

Let smaller rectangle EBCF, EB=t, AE=1-t, suppose EBCF is installed in AEFD,

E on AD and B on AE of larger. AE=1-t. <ABE =x

(1-t)= t cosx+ 1 sinx,...<1>, 1=t sinx + 1 cosx...<2>

From <1>, <2> 1-cos^2 x=sinx-sin^2 x, sinx=0, sinx=1/2

t=2-3^(1/2)