Explanation:

Converting complementary angles first, we get the target expression E as,
E=1/sin⁴(900−θ)+1/(cos²(900−θ)−1)
=1/cos⁴θ+1/(sin²θ−1).
Then it is straightforward trigonometric simplification,
E=1/cos⁴θ−1/cos²θ, coverting 1−sin²θ to cos²θ,
=1(sec²θ−1)/cos²θ
=tan²θsec²θ.