N is the smallest angle, in radians, of a triangle with side lengths 4, 5, and 41−810.
The following integral I is equal to δπα+βγ, for positive square-free integers α and γ and positive integers β and δ. What is α+β+γ+δ?
I=∫0Nsec4θ−tan4θsec4θ dθ
Details and Assumptions
There is exactly one place in this problem where you may need to use a four-function calculator.