(Calculus) As shown in the figure, for a positive angle $\theta$, there is an isosceles triangle ABC with $\angle \mathrm { ABC } = \angle \mathrm { ACB } = \theta$ and $\overline { \mathrm { BC } } = 2$. Let O be the center of the inscribed circle of triangle ABC, D be the point where segment AB meets the inscribed circle, and E be the point where segment AC meets the inscribed circle. [3 points] (1) $\frac { \pi } { 4 } - 1$ (2) $\frac { \pi } { 4 }$ (3) $\frac { \pi } { 4 } + \frac { 1 } { 3 }$ (4) $\frac { \pi } { 4 } + \frac { 1 } { 2 }$ (5) $\frac { \pi } { 4 } + 1$
(Calculus) As shown in the figure, for a positive angle $\theta$, there is an isosceles triangle ABC with $\angle \mathrm { ABC } = \angle \mathrm { ACB } = \theta$ and $\overline { \mathrm { BC } } = 2$. Let O be the center of the inscribed circle of triangle ABC, D be the point where segment AB meets the inscribed circle, and E be the point where segment AC meets the inscribed circle. [3 points]\\
(1) $\frac { \pi } { 4 } - 1$\\
(2) $\frac { \pi } { 4 }$\\
(3) $\frac { \pi } { 4 } + \frac { 1 } { 3 }$\\
(4) $\frac { \pi } { 4 } + \frac { 1 } { 2 }$\\
(5) $\frac { \pi } { 4 } + 1$