Quadratic and Trigonometry for JEE #1

Algebra Level 5

The number of integers \(b\) that satisfy the following condition is \( n: \)

The equation \[ \mid \sin x \mid ^{2} + \mid \sin x \mid + b =0 \] has two distinct real roots in the interval [0, \(\pi\)].

Find \( n^2 + n \).

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