71. In a convex hexagon $A B C D E F$, where $|A B|=|B C|,|C D|=|D E|,|E F|=|F A|$, the angles $\hat{B}=\alpha, \hat{D}=\beta, \hat{F}=\gamma$ are known. Determine the angles of triangle $B D F$, if $\alpha+\beta+\gamma=2 \pi$.
71. Let $K$ be the point of intersection of the circle centered at $B$ with radius $|A B|$ and the circle centered at $F$ with radius $|A F|$. Then $\widehat{A K C}=180^{\circ}-\frac{\alpha}{2}, \widehat{A K E}=180^{\circ}-\frac{\gamma}{2}$; considering the condition, we get that $\widehat{C K E}=180^{\circ}-\frac{\beta}{2}$; hence, $K$ lies on the circle centered at $D$ with radius $|C D|$. Therefore, $\widehat{K B F}=\widehat{A B F}$, $\widehat{K B D}=\widehat{C B D}$, i.e., $\widehat{F B D}=\frac{1}{2} \widehat{A B C}=\frac{\alpha}{2}$.

Answer: $\frac{\alpha}{2}, \frac{\beta}{2}, \frac{\gamma}{2}$.