For every θ, the expression co$s^4$θ + si$n^2$θ is identical to:

Put $c$ = co$s^2$θ, so si$n^2$θ = $1-c$ and the expression is $c^2-c+1$. Doing the same with $s$ = si$n^2$θ turns si$n^4$θ + co$s^2$θ into $s^2-s+1$, and $s=1-c$ leaves $(1-c{)}^2-(1-c)+1=c^2-c+1$ as well, so the two are always equal. Check at θ = 30°: 0.5625 + 0.25 = 0.8125 and 0.0625 + 0.75 = 0.8125. It is not the constant 1 — the fourth power spoils the Pythagorean cancellation.