\[g(\theta)=\left(\tfrac{1}{4}-\alpha^{2}\right)\left(\cot\left(\tfrac{1}{2}%
\theta\right)-\left(\tfrac{1}{2}\theta\right)^{-1}\right)-\left(\tfrac{1}{4}-%
\beta^{2}\right)\tan\left(\tfrac{1}{2}\theta\right).\]