If \( \cot \alpha \) equals the integral solution of inequality \( ...

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If \( \cot \alpha \) equals the integral solution of inequality \( 4 x^{2}-16 x+150 \) and \( \sin \beta \) equals to the slope of the bisector of the first quadrant, then \( \sin (\alpha+\beta) \sin (\alpha-\beta) \) is equal to :
\( \mathrm{P} \)
(a) \( -\frac{3}{5} \)
(b) \( -\frac{4}{5} \)
(c) \( \frac{2}{\sqrt{2}} \)
(d) 3
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