[填空题]
The diagram below shal ce, 6rj7hvq.d)t 5y2ua zc5ows j6/ez hdm3ph3+c,ci va fenced triangular enclosure in the middle of a grassy field where hjd/,mhz+c3c 3i p6ve $\mathrm{AC}=3 \mathrm{~m}, \mathrm{DC}=2 \mathrm{~m}, \mathrm{CB} \mathrm{A}=\alpha $ radians and $ \mathrm{AC} \hat{\mathrm{CB}}=\frac{\pi}{3} $ radians. One end of a rope is attached at point D on the outside edge of the enclosure, and the other end is attached to a goat G . Given that the rope is 6 $\mathrm{~m}$ long and the area of field outside the enclosure that the goat is able to graze is 74 $\mathrm{~m}^{2}$ , find the value of $\alpha$ .≈
