The expression co$s^4$θ − si$n^4$θ + 1 is equal to:

co$s^4$θ − si$n^4$θ = (co$s^2$θ − si$n^2$θ)(co$s^2$θ + si$n^2$θ) = co$s^2$θ − si$n^2$θ. Adding 1 = co$s^2$θ + si$n^2$θ makes the si$n^2$θ terms cancel, leaving 2co$s^2$θ.