In triangle ABC if tan A=(1)/(2),tan B=k...

In `triangle ABC` if `tan A=(1)/(2),tan B=k+(1)/(2)` and `tan C=2k+(1)/(2)`, and if the only possible value of `k` is `(p)/(q)` ,then the value of `p+q` ,(where `p` and `q` are co-prime) is

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