$\cot \left(\operatorname{Arctan} \frac{3}{5}\right)$

Step 1 ：The problem is asking for the cotangent of the arctangent of \(\frac{3}{5}\). The arctangent of a number is the angle whose tangent is that number. The cotangent of an angle is the reciprocal of the tangent of that angle. So, we need to find the reciprocal of the tangent of the angle whose tangent is \(\frac{3}{5}\).

Step 2 ：First, we find the arctangent of \(\frac{3}{5}\), which gives us an angle of approximately 0.5404195002705842.

Step 3 ：Next, we find the cotangent of this angle, which is the reciprocal of the tangent of the angle. This gives us a value of approximately 1.6666666666666667.

Step 4 ：Thus, the cotangent of the arctangent of \(\frac{3}{5}\) is approximately 1.6666666666666667.

Step 5 ：Final Answer: \(\boxed{1.6666666666666667}\)