HMMT 2019 T3

For any angle $0<\theta<\pi / 2$ , show that

$0<\sin \theta+\cos \theta+\tan \theta+\cot \theta-\sec \theta-\csc \theta<1$

Dataset text NuminaMath olympiads. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.