Point O is taken in square ABCD so that AOB is an equilateral triangle. Find the COD angle.

Since ABCD is a square, then AB = BC = CD = AD.
The ADP triangle, by condition, is equilateral, AO = DO = AD.
Then in the triangle AOB AB = AO, in the triangle COD OC = OD, then the triangles AOB and COD are isosceles.
In the triangle AOD, all internal angles are 600, then the angle CDO = CDA – ODA = 90 – 60 = 30.
In the CDO triangle, the angle is DOC = DCO = (180 – 30) / 2 = 150/2 = 75.
Answer: The COD angle is 750.