College Euclidean Geometry

[chaotixmonjuish]

I have this question:

Inside a square ABDE, take a point C so that CDE is an isosceles triangle with angles 15 degrees at D and E. What kind of triangle is ABC?

I put C close to the bottom to get my isosceles triangle. According to the answer in back, the triangle ABC is equilateral. The hint that went along with the answer is pick a point F to make a triangle congruent to triangle CDE. Are there theorems that I am missing to see how this could work out? I've spent a while on this and I feel like I'm missing something obvious.

[mathwonk]

have you tried law of cosines?

[chaotixmonjuish]

In this excercise, I have to do the proof using various Euclidean theorems. It's a practice excercise from Coxeter's Geometry book. The hint says to create a point F such that BF is perpendicular to CD aof the equilateral triangle CDF. Hence BC=BD=AB: and ABC is equilateral

I'm not sure how that happens