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Find the sum tantheta+1/2tantheta/2+1/(2...

Find the sum `tantheta+1/2tantheta/2+1/(2^2)tantheta/(2^2)+1/(2^3)tantheta/(2^3)+oo` and hence the sum of the series `1//2^2tanpi/(2^2)+1//2^3tanpi/(2^3)+1/(2^4)tanpi/(2^4)+oo`

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