NoNo it isn't a good news , i am interested in your ' techniques of integration' and waiting for your new posts .

i have a method but it's quite complicated , hope you dont mind it .

i first considered the infinite product of sine function :

Then take natural log. for each side , followed by differentiation , i got

Then

Consider

Thus , from the third step , i got

--- (1)

Square both ,

just consider the right hand side , it becomes

From (1) , i got

Then compare the coefficient of

,

the identity

is found

Also compare the coefficient of

As we have the identity , the value of

can be easily found , here is my result :