Find the value of the given expression:
$$1-\frac{7}{1-\frac{1}{1+\frac{7}{1-7}}}$$

Simplify the complex fraction step-by-step from the bottommost level upward:
$$1-\frac{7}{1-\frac{1}{1+\frac{7}{1-7}}}$$

Step 1: Simplify the bottommost denominator

$$1-7=-6$$

Now replace it back in the expression:

$$1+\frac{7}{-6}=1-\frac{7}{6}=\frac{6-7}{6}=-\frac{1}{6}$$

Step 2: Move up to the next level of fraction

$$\frac{1}{-\frac{1}{6}}=-6$$

Now update the expression layout:

$$1-(-6)=1+6=7$$

Step 3: Solve the main fraction block
Now the expression simplifies to:

$$1-\frac{7}{7}$$

$$1-1=0$$