How do you solve sec^2x-2=0?

The general solution is ##npi+-pi/3##
As ##sec^2x-2=0## we have
##sec^2x-(sqrt2)^2=0## or
##(secx+sqrt2)(secx-sqrt2)=0## and
##secx=+-sqrt2=+-sec(pi/3)##
Hence in the range ##(-pi+pi)## the values are ##{+-pi/3+-(2pi)/3}## which can also be written as ##{+-pi/3+-(pi-pi/3)}##
Hence the general solution is ##npi+-pi/3##