$\csc \left(\arctan \left(\frac{6}{3}\right)\right)$

Step 1 ：First, we need to find the arctangent of \(\frac{6}{3}\), which is the angle whose tangent is \(\frac{6}{3}\).

Step 2 ：Using a calculator, we find that the arctangent of \(\frac{6}{3}\) is approximately 1.1071487177940904.

Step 3 ：Next, we need to find the sine of this angle. Using a calculator, we find that the sine of 1.1071487177940904 is approximately 0.8944271909999159.

Step 4 ：Finally, we need to find the reciprocal of this sine value, which is the cosecant of the angle. The reciprocal of 0.8944271909999159 is approximately 1.118033988749895.

Step 5 ：So, the cosecant of the arctangent of \(\frac{6}{3}\) is approximately \(\boxed{1.118033988749895}\).