If the equation `sin ^(2) x - k sin x - 3 = 0` has exactly two distinct real roots in `[0, pi]`, then find the values of k .

Explanation

To solve the equation \( \sin^2 x - k \sin x - 3 = 0 \) for the values of \( k \) such that the equation has exactly two distinct real roots in the interval \([0, \pi]\), we can follow these steps:

### Step 1: Substitute \( t = \sin x \)
Since \( x \) is in the interval \([0, \pi]\), \( t \) will take values in the interval \([0, 1]\). Thus, we can rewrite the equation as:
\[ t^2 - kt - 3 = 0 \]

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