If sum of all the solutions of the equat...

If sum of all the solutions of the equation `(4tan x+tan^(2)x+1)=2sqrt(2)sin(x+(pi)/(4))(1+tan^(2)x)` in `[0,pi]` is `(p, (pi)/(q))` where `p,q` are relatively prime number, then find the value of `(p+q)`

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