Given a triangle `A B C` with sides a=7, b=8 and c=5. Find the value of expression `(sinA+sinB+sinC)(cot A/2+cotB/2+cotC/2)`

Explanation

`(a/(2R)+b/(2R)+c/(2R))((s(s-a))/ /_+(s(s-b))/ /_+(s(s-c))/ /_)`

`((a+b+c)/(2R))((s(3s-a+b+c))/ /_)`

`((2S)/(2R))((S*S)/ /_)`

`((2S)/(2R))(s^2/ /_)`

`s^3/(R/_)`

`4/(abc)((a+b+c)/2)^3`

`4/(7*8*5)((7+8+5)/2)^3`

`100/7`.