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 will follow these steps:

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

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