$$\begin{aligned} X(\mu,\theta,\theta_1) &= \frac{\displaystyle\frac{ 2\mu\Bigl[ 1+2\mu\cot\dfrac{\theta_1}{2}-\mu^2 +\left(\cot\dfrac{\theta_1}{2}-\mu\right) \left(\cot\dfrac{\theta}{2}-\mu\right) \Bigr] }{ \left(1+2\mu\cot\dfrac{\theta_1}{2}-\mu^2\right) \Bigl[ \left(\cot\dfrac{\theta}{2}-\mu\right)^2 +1+2\mu\cot\dfrac{\theta_1}{2}-\mu^2 \Bigr]^2 } -\frac{ \left(\cot\dfrac{\theta}{2}-\mu\right) \left(1+2\mu^2-\mu\cot\dfrac{\theta_1}{2}\right) }{ \left(1+2\mu\cot\dfrac{\theta_1}{2}-\mu^2\right)^2 \Bigl[ \left(\cot\dfrac{\theta}{2}-\mu\right)^2 +1+2\mu\cot\dfrac{\theta_1}{2}-\mu^2 \Bigr] } +\frac{ 1+2\mu^2-\mu\cot\dfrac{\theta_1}{2} }{ \left(1+2\mu\cot\dfrac{\theta_1}{2}-\mu^2\right)^{5/2} } \left[ \frac{\pi}{2} -\arctan\!\frac{ \cot\dfrac{\theta}{2}-\mu }{ \sqrt{1+2\mu\cot\dfrac{\theta_1}{2}-\mu^2} } \right]}{\displaystyle\frac{ \mu^2\cot\dfrac{\theta_1}{2} +\mu\cot^2\dfrac{\theta_1}{2} +3\mu -\cot\dfrac{\theta_1}{2} }{ \csc^2\dfrac{\theta_1}{2} \left(1+2\mu\cot\dfrac{\theta_1}{2}-\mu^2\right)^2 } +\frac{ 1+2\mu^2-\mu\cot\dfrac{\theta_1}{2} }{ \left(1+2\mu\cot\dfrac{\theta_1}{2}-\mu^2\right)^{5/2} } \left[ \frac{\pi}{2} -\arctan\!\frac{ \cot\dfrac{\theta_1}{2}-\mu }{ \sqrt{1+2\mu\cot\dfrac{\theta_1}{2}-\mu^2} } \right]} \end{aligned}$$$$\begin{aligned} Y(\mu,\theta,\theta_1) &= \frac{\displaystyle\frac{ 2\mu\Biggl[ \left(1+2\mu\cot\dfrac{\theta_1}{2}-\mu^2\right) \left(2\mu-\cot\dfrac{\theta_1}{2}\right) +\left(1-2\mu^2+3\mu\cot\dfrac{\theta_1}{2}\right) \left(\cot\dfrac{\theta}{2}-\mu\right) \Biggr] }{ \left(1+2\mu\cot\dfrac{\theta_1}{2}-\mu^2\right) \Bigl[ \left(\cot\dfrac{\theta}{2}-\mu\right)^2 +1+2\mu\cot\dfrac{\theta_1}{2}-\mu^2 \Bigr]^2 } +\frac{ \left(1+2\mu\cot\dfrac{\theta_1}{2}-\mu^2\right)^2 -\mu\left(2+\mu^2+\mu\cot\dfrac{\theta_1}{2}\right) \left(\cot\dfrac{\theta}{2}-\mu\right) }{ \left(1+2\mu\cot\dfrac{\theta_1}{2}-\mu^2\right)^2 \Bigl[ \left(\cot\dfrac{\theta}{2}-\mu\right)^2 +1+2\mu\cot\dfrac{\theta_1}{2}-\mu^2 \Bigr] } +\frac{ \mu\left(2+\mu^2+\mu\cot\dfrac{\theta_1}{2}\right) }{ \left(1+2\mu\cot\dfrac{\theta_1}{2}-\mu^2\right)^{5/2} } \left[ \frac{\pi}{2} -\arctan\!\frac{ \cot\dfrac{\theta}{2}-\mu }{ \sqrt{1+2\mu\cot\dfrac{\theta_1}{2}-\mu^2} } \right]}{\displaystyle\frac{ \mu^2\cot\dfrac{\theta_1}{2} +\mu\cot^2\dfrac{\theta_1}{2} +3\mu -\cot\dfrac{\theta_1}{2} }{ \csc^2\dfrac{\theta_1}{2} \left(1+2\mu\cot\dfrac{\theta_1}{2}-\mu^2\right)^2 } +\frac{ 1+2\mu^2-\mu\cot\dfrac{\theta_1}{2} }{ \left(1+2\mu\cot\dfrac{\theta_1}{2}-\mu^2\right)^{5/2} } \left[ \frac{\pi}{2} -\arctan\!\frac{ \cot\dfrac{\theta_1}{2}-\mu }{ \sqrt{1+2\mu\cot\dfrac{\theta_1}{2}-\mu^2} } \right]} \end{aligned}$$

其中 $\theta_1$ 满足

$$\begin{aligned} &\frac{\displaystyle \frac{ 3\mu^2\cot^2\dfrac{\theta_1}{2} +2\mu^2 +2\mu\cot\dfrac{\theta_1}{2} +1 }{ \csc^2\dfrac{\theta_1}{2} \left(1+2\mu\cot\dfrac{\theta_1}{2}-\mu^2\right)^2 } +\frac{ \mu\left(2+\mu^2+\mu\cot\dfrac{\theta_1}{2}\right) }{ \left(1+2\mu\cot\dfrac{\theta_1}{2}-\mu^2\right)^{5/2} } \left[ \frac{\pi}{2} -\arctan\!\frac{ \cot\dfrac{\theta_1}{2}-\mu }{ \sqrt{1+2\mu\cot\dfrac{\theta_1}{2}-\mu^2} } \right] }{\displaystyle \frac{ \mu^2\cot\dfrac{\theta_1}{2} +\mu\cot^2\dfrac{\theta_1}{2} +3\mu -\cot\dfrac{\theta_1}{2} }{ \csc^2\dfrac{\theta_1}{2} \left(1+2\mu\cot\dfrac{\theta_1}{2}-\mu^2\right)^2 } +\frac{ 1+2\mu^2-\mu\cot\dfrac{\theta_1}{2} }{ \left(1+2\mu\cot\dfrac{\theta_1}{2}-\mu^2\right)^{5/2} } \left[ \frac{\pi}{2} -\arctan\!\frac{ \cot\dfrac{\theta_1}{2}-\mu }{ \sqrt{1+2\mu\cot\dfrac{\theta_1}{2}-\mu^2} } \right] } =\frac{b}{a}. \end{aligned}$$