shortest distance between two cones in 3-dim space

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How can I find the shortest distance between two cones in 3-dim space?

cone 1:

apex - $(x_{0}, y_{0}, z_{0})$

angle - $\alpha_{0}$

base circle - $(cx_{0}, cy_{0}, cz_{0}, r_{0})$

cone 2:

apex - $(x_{1}, y_{1}, z_{1})$

angle - $\alpha_{1}$

base circle - $(cx_{1}, cy_{1}, cz_{1}, r_{1})$