How to calculate angles in three dimensional planes given the speed and angle?

I want to calculate what angle a three dimensional vector makes with respect to x-y plane, y-z plane and z-x plane when only the speed and the direction of the speed (i.e. the angle between the direction of the speed and the x-axis) is given. There is this equation cos^2(theta)+cos^2(phi)+cos^2(upsilon)=1 but I cannot use this equation as all three angles theta, phi and upsilon are my unknowns. Only the magnitude of three-dimensional speed and its angle wrt the x-axis is known.