What is $\rm \frac{\cos 17^\circ-\sin 17^\circ}{\cos 17^\circ+\sin ^\circ}$ equal to

Consider the following numbers : 

I. tan 22.5° 

II. cot 22.5° 

III. tan 22.5° - cot 22.5° 

How many of the above are irrational numbers?

If $\rm \frac{x}{\cos \theta}=\frac{y}{\cos \left(\frac{2\pi}{3}-\theta\right)}=\frac{z}{\cos\left(\frac{2\pi}{3}+\theta\right)}$ then what is x + y + z equal to? 

If p tan (θ - 30°) = q tan (θ + 120°), then what is (p + q) / (p - q) equal to?