Squeezing Range

Level pending

If \( f(x) = x^3 - 2x^2 \sin \theta + x + 1 \; (0 \leq \theta \leq \pi) \) has both a local maximum and a local minimum, the range of \(\theta\) can be restricted further by \( a \pi < \theta < b \pi\). What is the value of \(30(b-a)?\)

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