separation constant

The partial differential equation a sin ²(𝜃)𝛷(𝜙)+𝛷(𝜙) cos (𝜃)(∂𝛩(𝜃))/(∂𝜃)+(∂²𝛷)/(∂𝜙²)=0 can be rewritten a sin ²(𝜃)+ cos (𝜃)(∂𝛩(𝜃))/(∂𝜃)=-1/(𝛷(𝜙))(∂²𝛷)/(∂𝜙²)≡K, where K is a separation constant that depends on neither 𝜃 nor 𝜙. This then yields two ordinary differential equations.