How good are you with Triangles!

Geometry Level 5

\[π\left(\large\sum_{}^{a,b,c} \frac{a}{bc[\sin(C-A)\sin(A-B)(\sin B + \sin C)]}\right)\]

Consider a \(\triangle ABC\). Find the above summation up to 3 decimal places. Here the summation is a cyclic summation i.e the \(a\) in the first term becomes \(b\) in the second and \(c\) in the third. The same holds for angles.

If you think the above sum is not a constant for a given triangle then type 0.22 as your answer.

Note: \( A \ne B \ne C \) or\(A,B,C\) are distinct .

Feel this is a bit difficult ,try this problem

This problem is a modified one, from a book written by S.L. Loney.


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