Question 5
In equilateral $\triangle ABC$ let points $D$ and $E$ trisect $\overline{BC}.$ Then $\sin(\angle DAE)$ can be expressed in the form $\frac{a\sqrt{b}}{c},$ where $a$ and $c$ are relatively prime positive integers, and $b$ is an integer that is not divisible by the square of any prime. Find $a + b + c.$