Angle between two lines

I have the following geometry:

All the blues and whites are known. The reds are to be determined (specifically speaking θ).

Any help would be appreicted.

Thanks.

Answer 1

[Jan]

This cannot work. There is no realtion between Theta and Phi. Therefore the parameters to define the blue line does not allow to define the red one.

The question would be meaningful (and easy to solve), if the red line is orthogonal to the blue one.

By the way, even if the question contains enough information, you'd have to show us, in which format the line is defined.