<Tri-2023-2026>, hint

Let A(3) be O. Since O is the center of rotation, 60 degrees

triangles A(1)B(1)C(1) and A(2)B(2)C(2) are congruent and O is the circumcenter of

the above two triangles. M and N are the mass centers of the two triangles.

Hence OM=ON <MON=60 degrees, equilateral