If tanθ + cotθ = 4, then the value of ta$n^4$θ + co$t^4$θ is:

Square the given equation: ta$n^2$θ + co$t^2$θ + 2·tanθ·cotθ = 16, and tanθ·cotθ = 1, so ta$n^2$θ + co$t^2$θ = 14. Square again: ta$n^4$θ + co$t^4$θ + 2 = 196, so the value is 194. Stopping at the halfway result reports 14, forgetting the final −2 gives 196, and squaring the given number twice over gives $4^4-2=254$.