If $α + β = \frac{\pi}{4}$ and 2tan α = 1, then what is tan 2β equal to?

If tan (45° + θ) = 1 + sin 2θ, where $-\frac{\pi}{4}< θ <\frac{\pi}{4},$ then what is the value of cos 2θ?

Let sin 2θ = cos 3θ, where θ is acute angle. What is the value of 1 + 4 sin θ? (given that $\sin 18^\circ =\frac{\sqrt 5 - 1}{4}$)

If $\tan θ = - \frac{5}{12},$ then what can be the value of sin θ?