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Given four non zero vectors vec a ,vec ...

Given four non zero vectors `vec a ,vec b, vec c and vec d`.The vectors `vec a ,vec b and vec c` are coplanar but not collinear pair by pair and vector `vec d` is not coplanar with vector `vec a ,vec b and vec c and hat(vec a vec b)=hat (vec b vec c)=pi/3,hat (vec d vec a)=alpha,hat (vec d vec b)=beta`, then prove that `hat(vec d vec c)=cos^-1(cos beta-cosalpha)`

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