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sec^6x-tan^6x-3sec^2x*tan^2x=1 how to prove this identity

sec⁶θ - tan⁶θ - 3secēθtanēθ = (secēθ -tanēθ) (sec⁴θ + secēθtanēθ + tanēθ) - 3secēθtanēθ

= ((1+tanēθ) - tanēθ) (sec⁴θ + secēθtanēθ + tanēθ) - 3secēθtanēθ

= (1) (sec⁴θ + secēθtanēθ + tanēθ) - 3secēθtanēθ

= sec⁴θ - 2secēθtanēθ + tanēθ

= (secēθ - tanēθ)ē

= 1ē

= 1

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