Are theta_rotor, theta_stator, and u_axial all known values? If not, then no, fsolve cannot solve it. But if we assume those are known parameters, then you can do a LOT of work yourself. In fact, it appears as if a solution does exist that we can do by hand.
Write the first equation as
u_blade/u_axial = tan(theta_stator) + tan(b2)
Now, add theta_rotor to both sides of (2), then take the tan. This gives us
tan(b2 + theta_rotor) = u_blade/u_axial
But we already have the ratio of u_blade to u_axial, so eliminate them to get only one equation in the unknown b2.
tan(b2 + theta_rotor) = tan(theta_stator) + tan(b2)
Again, theta_rotor and theta_stator are knowns. We now go to a table of trig identities, to get the tan of a sum of terms, and we can expand the left hand side.
Or, I can just be lazy as hell, and let MATLAB do the work.
syms b2 theta_rotor theta_stator
bssol = solve( tan(b2 + theta_rotor) == tan(theta_stator) + tan(b2),b2)
Once you know b2 (It is completely given there, as two distinct solutions, now you can trivially return to recover u_blade.
Why bother with fsolve, when an analytial solution is available? I hardly needed MATLAB at all, until I got too lazy at the end. But pencil and paper would have been sufficient. Note that had I just fed these two equations directly into solve, then solve should have been able to find the solution on its own. But would that have been any fun?
