If the distance between two points  (acosθ,asinθ) and (acosϕ,asinϕ) is 2a then  θ is

(acosθ−acosϕ)2+(asinθ−asinϕ)2=4a2⇒−2a2cos(θ−ϕ)=4a2−2a2⇒cos(θ−ϕ)=−1⇒θ−ϕ=2nπ±π⇒θ=2nπ±π+ϕ,n∈Z