\begin{table}%t7
%\centering
\par
\caption{Expressions for the coefficients of the precession 
quantities.\label{tab7}}
\renewcommand{\arraystretch}{1.25}
$$
\begin{tabular}{ccll}
\hline\hline
Quantity &  Coefficient of $t$ & Coefficient of $t^2$ &Coefficient of $t^3$ \\
\hline\noalign{\smallskip}
$\psi_{\rm A}$ & $r_0$ & $\displaystyle\frac{1}{2} \left(r_1 +r_0c_1\cot\epsilon_0 -\frac{u_0s_1}{\sin^2\epsilon_0}\right)$
& $\displaystyle\frac{1}{3}\left[ r_2 + \cot\epsilon_0 \left(r_0c_2-r_0^2s_1+r_1c_1\right)\right]$
$\displaystyle-\frac{1}{6} r_0\left(c_1^2 +\frac{s_1^2}{\sin^2\epsilon_0}\right)
$\\ &&&$\displaystyle +\frac{1}{3}\left(\cot\epsilon_0 /\sin^2\epsilon_0\right)\left(u_0c_1s_1+u_0^2s_1\right)
$\\ &&&$\displaystyle -\frac{1}{3\sin^2\epsilon_0} \left(r_0u_0c_1+u_0s_2+u_1s_1\right)$ \\
\noalign{\smallskip}\hline\noalign{\smallskip}
$\omega_{\rm A}$ & $u_0$ & $\displaystyle\frac{1}{2}(u_1+r_0s_1)$ & $\displaystyle\frac{1}{3} \left[
u_2+r_1s_1+r_0s_2+c_1r_0^2 - \frac{u_0s_1^2}{2 \sin^2\epsilon_0} \right] $  \\
\noalign{\smallskip}\hline\noalign{\smallskip}
$\epsilon_{\rm A}$  & $c_1+u_0$ & $ \displaystyle c_2+\frac{1}{2} \left(u_1-s_1 r_0+ s_1^2 \cot\epsilon_0\right)$ & $\displaystyle c_3+\frac{1}{3}u_2-\frac{2}{3}r_0s_2+s_1s_2\cot\epsilon_0
$\\ &&&$\displaystyle - \frac{1}{6}\left[ r_0^2c_1+r_1s_1+\frac{s_1^2(u_0+c_1)}{\sin^2\epsilon_0}\right]
$\\ &&&$\displaystyle + \frac{s_1 \cot\epsilon_0}{2}\left(r_0c_1-c_1s_1\cot\epsilon_0\right)$ \\
\noalign{\smallskip}\hline\noalign{\smallskip}
$\chi_{\rm A}$ & $s_1/\sin\epsilon_0$ &
$\displaystyle \frac{1}{\sin\epsilon_0}\left[ s_2+r_0c_1- s_1\cot\epsilon_0(u_0+c_1) \right]$ &
$ \displaystyle\frac{1}{\sin\epsilon_0}\left[ s_3 + r_0 \left[ c_2-\frac{1}{2}r_0s_1+\left(\frac{1}{2}s_1^2-u_0c_1\right)\cot\epsilon_0 \right]
\right.$\\ &&&$\displaystyle\left. - \left(s_1s_2 + u_0s_2 +c_2s_2\right)\cot\epsilon_0
\right.$\\ &&&$\displaystyle\left. -\frac{1}{2}\left(s_1u_1+s_1c_2 +c_1^2s_1 \cot\epsilon_0\right) \cot\epsilon_0
\right.$\\ &&&$\displaystyle\left. + \frac{1}{2} r_1c_1+s_1c_1^2 + \frac{1}{\sin^2\epsilon_0}u_0c_1s_1
\right.$\\ &&&$\displaystyle\left.  + \frac{s_1^3}{\sin^3\epsilon_0}\left(\frac{1}{6}-\frac{1}{2}\cos\epsilon_0^2\right)
+u_0^2s_1\left(\frac{1}{2} + \cot\epsilon_0^2\right) \right] $ \\
\noalign{\smallskip}\hline\noalign{\smallskip}
$p_{\rm A}$  &$r_0-s_1\cot\epsilon_0$ & $\displaystyle\frac{1}{2} \left(r_1 - r_0c_1\cot\epsilon_0 + \frac{u_0s_1}{\sin^2\epsilon_0}\right)- s_2\cot\epsilon_0 
$ &
$ \displaystyle-s_3\cot\epsilon_0 - \frac{u_0c_1s_1}{2\sin^2\epsilon_0}\cot\epsilon_0
$\\ &&$\displaystyle +\frac{s_1 c_1}{2}\left(1+2\cot^2\epsilon_0\right)$&$ + \frac{1}{3} \left[ r_2 + \cot\epsilon_0\left(c_1s_2\cot\epsilon_0-r_0c_2+s_2c_1\right) \right]
$\\ &&&$\displaystyle + \frac{1}{3\sin^2\epsilon_0}\left(2c_2s_1-u_0^2s_1+2s_2u_0+s_2c_1\right)
$\\ &&&$\displaystyle - \frac{1}{6}\left[ \left(r_1^2s_1-r_1c_1\right)\cot\epsilon_0 - r_0c_1^2+r_0s_1^2 \right]
$\\ &&&$\displaystyle + \frac{1}{6\sin^2\epsilon_0}\left[ \left(s_1^3-c_1^2s_1\right)\cot\epsilon_0 +s_1u_1 \right]$  \\
\noalign{\smallskip}\hline
\end{tabular}$$
\end{table}