Given a triangle \( A B C \) with sides \( a=7, b=8 \) and \( c=5 \...

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Given a triangle \( A B C \) with sides \( a=7, b=8 \) and \( c=5 \). If the value of the expression
\( \mathrm{P} \) \( \left(\sum \sin A\right)\left(\sum \cot \frac{A}{2}\right) \) can be expressed in the form \( \frac{p}{q} \) where \( p, q \in N \) and \( \frac{p}{q} \) is in its lowest form find

W the value of \( (p+q) \).
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