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If P=x+1/x and P(tan alpha)=2, P(tan bet...

If `P=x+1/x` and `P(tan alpha)=2, P(tan beta)=2sqrt2, P(cot gamma)=4` where `alpha, beta, gamma` are acute angles and sum of all possible distinct values of `alpha, beta` and `gamma `is given by `(mpi)/n` where `m` and `n` are coprime, then find the value of `(m+n)`

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