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MathNet 2015-part-01 — 191 problems (EN–VI) Question 2

Math Olympiad Vault · MathNet 2015-part-01 — 191 problems (EN–VI)

Question 2

Points $D$ and $E$ divide side $AB$ of equilateral triangle $ABC$ into three equal parts; $D$ is between $A$ and $E$. Point $F$ on side $BC$ is such that $CF = AD$. Find the sum of the angles
$$
C\hat{D}F + C\hat{E}F.
$$