Suppose that $\theta$ is an angle in standard position whose terminal side intersects the unit circle at $\left(-\frac{2 \sqrt{6}}{7},-\frac{5}{7}\right)$ Find the exact values of $\sin \theta, \sec \theta$, and $\tan \theta$. \[ \begin{array}{l} \sin \theta=\square \\ \sec \theta=\square \\ \tan \theta=\square \end{array} \] \begin{tabular}{|c|c|c|} \hline 믐 & $\sqrt{\square}$ & \\ \hline$x$ & & 5 \\ \hline \end{tabular}

Step 1 ：\(\sin \theta = -\frac{5}{7}\)

Step 2 ：\(\sec \theta = \frac{1}{\cos \theta} = \frac{1}{-\frac{2 \sqrt{6}}{7}} = -\frac{7}{2 \sqrt{6}}\)

Step 3 ：\(\sec \theta = -\frac{7 \sqrt{6}}{12}\)

Step 4 ：\(\tan \theta = \frac{\sin \theta}{\cos \theta} = \frac{-\frac{5}{7}}{-\frac{2 \sqrt{6}}{7}} = \frac{5}{2 \sqrt{6}}\)

Step 5 ：\(\tan \theta = \frac{5 \sqrt{6}}{12}\)

Step 6 ：\(\boxed{\sin \theta = -\frac{5}{7}, \sec \theta = -\frac{7 \sqrt{6}}{12}, \tan \theta = \frac{5 \sqrt{6}}{12}}\)