Inverse of a parametric equation with two inputs

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I have two equations that make up a parametric set while taking two angles as an input. These equations are defined below:

x(θ1,θ2) = cos(θ1)+cos(θ1+θ2)
y(θ1,θ2) = sin(θ1)+sin(θ1+θ2)

Is there any way I can take the inverse of these equations such that I can input the x and y and get the θ1 and θ2 independent of each other?