# 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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