What are the fixed points of
$$ θ'=1-a\sinθ $$
$$\text{what type of bifurcation occurs at } a=1, \;\;\;θ=π/2 $$
Solution:
$$ 1/a=\sinθ \text{ or } θ=\arcsin(1/a) $$
I cant seem to find the proper fixed points after this step
What are the fixed points of
$$ θ'=1-a\sinθ $$
$$\text{what type of bifurcation occurs at } a=1, \;\;\;θ=π/2 $$
Solution:
$$ 1/a=\sinθ \text{ or } θ=\arcsin(1/a) $$
I cant seem to find the proper fixed points after this step
You don't need to find any fixed points analytically to get the answer you are seeking.
Plot the function $$ a=\frac{1}{\sin \theta} $$ in the interval $(\pi/2-\varepsilon,\pi/2+\varepsilon)$. Fixing $a=\hat{a}$ gets you an idea about the number of fixed points and their types (this is called bifurcation diagram).
Note that if $a>1$ then you have two fixed points, one is stable and another is unstable. If $a<1$ then you have no fixed points, the two above approached each other and collapsed. This should be known to you as a saddle-node, or tangent, or fold bifurcation.