16cos⁡θ−cos⁡π8cos⁡θ−cos⁡3π8cos⁡θ−cos⁡5π8cos⁡θ−cos⁡7π8=λcos⁡4θ then the value of λ is _____ .

16cos⁡θ−cos⁡π8cos⁡θ−cos⁡3π8cos⁡θ−cos⁡5π8×cos⁡θ−cos⁡7π8=16cos⁡θ−cos⁡π8cos⁡θ−cos⁡7π8×cos⁡θ−cos⁡3π8cos⁡θ−cos⁡5π8=16cos⁡θ−cos⁡π8cos⁡θ+cos⁡π8×cos⁡θ−cos⁡3π8cos⁡θ+cos⁡3π8=16cos2⁡θ−cos2⁡π8cos2⁡θ−cos2⁡3π8=16cos2⁡θ−cos2⁡π8cos2⁡θ−sin2⁡π8=16cos4⁡θ−cos2⁡θ+sin2⁡π8cos2⁡π8=16cos4⁡θ−cos2⁡θ+18=16−cos2⁡θsin2⁡θ+18=16−sin2⁡2θ4+18=161−2sin2⁡2θ8=16cos⁡4θ8