=> tan^{7}x+\frac{1}{tan^{7}x}-tanx-\frac{1}{tanx}=0
=> tanx(tan^{6}-1)+\frac{1}{tanx}(\frac{1}{tan^{6}x}-1)=0
=> tanx(tan^{6}-1)-\frac{1}{tanx}.\frac{tan^{6}x-1}{tan^{6}}=0
=> (tan^{6}x-1)(tanx-\frac{1}{tan^{7}x})=0
=> (tan^{6}x-1).\frac{tan^{8}x-1}{tan^{7}x}=0
=> ...........................