find the angle of intersection of the cardioid r=a (1+cos θ ) and r=b (1-cos θ)

a(1+cos{\theta})=b(1-cos{\theta})

{\theta}=\frac{(4C-1){\pi}}{2}-sin^{-1}(\frac{a-b}{a+b}) \;\ or \;\ sin^{-1}(\frac{a-b}{a+b})+\frac{(4C+1){\pi}}{2}

\frac{a-b}{a+b}\leq 1, \;\ \frac{a-b}{a+b}\geq -1

Let C=an integer and the angle theta depends on the values of a and b.

Try some arbitrary a and b values and check.