Last minute explanations on Trig Identities.

I’m ready for my Math Final…. except there are several things regarding Trig Identities that just don’t process for me. I picked several sample problems from my practice packet that just don’t click. If you can help me work through them it would be greatly appreciated:

1. What needs to be changed in the last two lines to make this correct?
line one: cos2x=.5
line two: 2x={ 30º+360nº
{ 180º-30º+360nº
line three: x={ 15º+360nº
{ 75º+360nº

2. solve 2sinxcosx=cosx where x is [-π, π]

3. solve tan2θ=-1.2 where 0<θ<360

4. (1-cotθ)^2=csc^2θ-2cotθ

5. (sinθ+cosθ)/cosθ-(sinθ-cosθ)/sinθ=secθcscθ