In a `triangleABC`, if `|(1,1,1),(1+sinA,1+sinB,1+sinC),(sinA+sin^2A,sinB+sin^2B,sinC+sin^2C)|=0`, then prove that `triangleABC` is an isosceles triangle.

Explanation

To prove that triangle ABC is isosceles given the determinant condition, we can follow these steps:

### Step 1: Write the Determinant
We start with the determinant given in the problem:

\[
D = \begin{vmatrix}
1 & 1 & 1 \\
...