[填空题]
The diagram below shows q;.r,zj8gul, ubr 9pu a fenced triangular enclosure in the middle of a gr3kp+:av(0 svek 8n wpkgy3 d4bassy field :nka+ep3 8 kdw4bvvg(s0y3pkwhere $\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 $\alpha$ .≈
