Question

r=sin(theta) and r=1-sin(theta)
give an ALGEBRAIC SOLUTION to all points of intersection

Answer 1

As it has been solved, theta = pi/6 or 5pi/6 between 0 and 2pi.
To get a general solution, we note that the two solutions are between pi/2, so it is
S={pi/2+/-pi/3+2kpi | k : integer}