For every θ at which both sides are defined, se$c^2$θ + cose$c^2$θ is equal to:

Over a common denominator, se$c^2$θ + cose$c^2$θ = (si$n^2$θ + co$s^2$θ)/(si$n^2$θ·co$s^2$θ) = 1/(si$n^2$θ·co$s^2$θ), which is exactly the product se$c^2$θ·cose$c^2$θ. Check at θ = 30°: 4/3 + 4 = 16/3 and $(4/3)\times 4=16/3$. The near miss ta$n^2$θ + co$t^2$θ equals (se$c^2$θ − 1) + (cose$c^2$θ − 1), i.e. the same sum less 2; and the value is certainly not the constant 1, since it is never smaller than 4.