Solve the equation `sin^(2)ntheta - sin^(2)(n-1)theta = sin^(2)theta`

Explanation

To solve the equation \( \sin^2(n\theta) - \sin^2((n-1)\theta) = \sin^2(\theta) \), we can follow these steps:

### Step 1: Rewrite the equation using the difference of squares
We can use the identity for the difference of squares, which states that \( a^2 - b^2 = (a-b)(a+b) \). Here, we let \( a = \sin(n\theta) \) and \( b = \sin((n-1)\theta) \).

\[ \sin^2(n\theta) - \sin^2((n-1)\theta) = (\sin(n\theta) - \sin((n-1)\theta))(\sin(n\theta) + \sin((n-1)\theta)) \]
...