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Answer 1 · 2017-03-23T20:48:43

#x={0,pi/4,3/4pi,pi,5/4pi,7/4pi,2pi}#

#tan^8 x -tan^4 x=tan^4x(tan^4x-1)=0#

so we have

#tan^4 x=0->tan x = 0#

and

#tan^4x-1=(tan^2x+1)(tan^2x-1)=(tan^2x+1)(tanx-1)(tanx+1)#

Here #tan^2x+1=0# is unfeasible so we will consider only

#{(tanx=0),(tanx=1),(tanx=-1):}#

and then

#x = kpi uu x=pi/4+kpiuux=3/4pi+kpi# for #k=0,1,2,cdots#

or

#x={0,pi/4,3/4pi,pi,5/4pi,7/4pi,2pi}#