In $\triangle A B C$, with usual notations, if $\frac{1}{b+c}+\frac{1}{c+a}=\frac{3}{a+b+c}$, then $m \angle C$ is equal to

In a triangle $$\mathrm{A B C, m \angle A, m \angle B, m \angle C}$$ are in A.P. and lengths of two larger sides are 10 units, 9 units respectively, then the length (in units) of the third side is

In $$\triangle \mathrm{ABC}$$, with usual notations, $$2 \mathrm{ac} \sin \left(\frac{1}{2}(\mathrm{~A}-\mathrm{B}+\mathrm{C})\right)$$ is equal to

If the angles $$\mathrm{A}, \mathrm{B}$$, and $$\mathrm{C}$$ of a triangle are in an Arithmetic Progression and if $$\mathrm{a}, \mathrm{b}$$ and $$\mathrm{c}$$ denote the lengths of the sides opposite to A, B and C respectively, then the value of the expression $$\frac{\mathrm{a}}{\mathrm{c}} \sin 2 \mathrm{C}+\frac{\mathrm{c}}{\mathrm{a}} \sin 2 \mathrm{~A}$$ is