Given:

Let's use a trig identity to find the value of tanθ.
Apply the definition of cosecant to find known sides of the unit circle.
We have:

Here, the hypotenuse and opposite sides are known.
Also, find the adjacent side using Pythagorean Theorem:
![\begin{gathered} \text{adjacent}=\sqrt[]{hypotenuse^2-opposite^2} \\ \\ \text{adjacent}=\sqrt[]{7^2-6^2} \\ \\ \text{adjacent}=\sqrt[]{49-36}=\sqrt[]{13} \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/aq3iz37pblb1l3ewwbhtjbx32gwqnapxy9.png)
Apply the definition of tangent to find tanθ:
![\begin{gathered} \tan \theta=\frac{opposite}{\text{adjacent}} \\ \\ \text{tan}\theta=\frac{6}{\sqrt[]{13}} \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/gx95avvsm8fwi0mhy89ixdkz9620gd76zz.png)
Simplify:
![\begin{gathered} \tan \theta=\frac{6}{\sqrt[]{13}}*\frac{\sqrt[]{13}}{\sqrt[]{13}} \\ \\ \tan \theta=\frac{6\sqrt[]{13}}{13}=1.664 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/ql6u7qwjecsicsfbgwuaj60dk69mrh3mxc.png)
ANSWER:
