For how many values of \alpha does the expression (\sin \alpha+2)(\sin \alpha+4)(\sin \alpha-2)(\sin \alpha-4) become zero?

Explanation

The expression equals zero if \sin \alpha \in \{-4, -2, 2, 4\}. Since the range of \sin \alpha is [-1, 1], there is no real value of \alpha that satisfies this condition.

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