Magnetic field varies as you rotate a wire- challenging problem!

A wire segment of length 4.75 cm carries a current of 3.46 A is placed between the poles of magnet. For one orientation of the wire in the field, the wire experiences a magnetic force of magnitude 0.375 N. By rotating the wire to several different orientations, it is found that for one particular orientation of the wire the force on the wire has its maximum value which is 3 times the original value.

Find:
a) the strength of the magnetic field
b) the angle between the two orientations of the wire

*Any help with this would be great, I'm not sure how to start!

(a) Max. force corresponds with wire perpendicular to the field
F(max) = 3*0.375 = 1.125 N

F(max) = BiL = 1.125 N
B= F(max) / iL = 1.125 /(3.46A * 0.0475 m) .. .. ►B = 6.85 T

(b) F1 = BiL sinθ (θ= angle between horiz. field and wire)(FI = 0.375 N)
sinθ = F1/BiL = 0.375 / (6.85T*3.46A*0.0475m) = 0.3333
θ = 19.47º

Angle between perp. and 19.47º = 90 - 19.47 .. .. ►= 70.53º