differential equations - How to solve these ODEs using NDSolve?

I have six odes and I cannot use DSolve. So I tried NDSolve. But it says there may be some errors.The code is such like this:

I1 = 2; I2 = 3; I3 = 4;
NDSolve[{I1*ω1'[t] + (I3 - I2)*ω2[t]*ω3[t] == 0, 
I2*ω2'[t] + (I1 - I3)*ω1[t]*ω3[t] == 0, 
I3*ω3'[t] + (I2 - I1)*ω2[t]*ω1[t] == 0, 
ω1[t] == φ'[t]*Sin[θ[t]]*Sin[ψ[t]] + θ'[t]*Cos[ψ[t]], 
ω2[t] == φ'[t]*Sin[θ[t]]*Cos[ψ[t]] - θ'[t]*Sin[ψ[t]], 
ω3[t] == φ'[t]*Cos[θ[t]] + ψ'[t], 
ω1[0] == 2, ω2[0] == 3, ω3[0] == 4, ψ[0] == 0, φ[0] == 0, θ[0] == Pi/6}, 
{ω1, ω2, ω3, ψ, φ, θ}, {t, 0, 120}]

I want to know how to avoid this error.