Find all the value of `m` for which the equation `sin^2x+(m-3)sinx+m=0` has real roots.

Explanation

To solve the equation \( \sin^2 x + (m - 3) \sin x + m = 0 \) for the values of \( m \) that allow for real roots, we can follow these steps:

### Step 1: Substitute \( t \) for \( \sin x \)
Let \( t = \sin x \). The equation then becomes:
\[ t^2 + (m - 3)t + m = 0 \]
where \( t \) must lie within the interval \([-1, 1]\).
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