First, we calculate $1 \nabla 2$: $$1 \nabla 2 = \frac{1 + 2}{1 + 1 \times 2} = \frac{3}{3} = 1.$$Next, we calculate $(1 \nabla 2) \nabla 3$: $$(1 \nabla 2) \nabla 3 = 1 \nabla 3 = \frac{1 + 3}{1 + 1 \times 3} = \frac{4}{4} = \boxed{1}.$$The answer is: 1
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
If $a>0$ and $b>0,$ a new operation $\nabla$ is defined as follows:  $$a \nabla b = \frac{a + b}{1 + ab}.$$For example, $$3 \nabla 6 = \frac{3 + 6}{1 + 3 \times 6} = \frac{9}{19}.$$Calculate $(1 \nabla 2) \nabla 3.$

### Answer:
