A basic three phase ,two pole Synchronus machine of the salient pole type has the following inductances,where θ is measured from d-axis to the axis of phase A.Phase A self-inductance , La=0.9+0.2cos2 θ, Mutual inductance between phase A and field winding F, $M_{af} = 8 cos \theta$ , Mutual inductance between phase B and C, $M_{bc} = -0.4 + 0.2 cos 2 \theta$

a) Write expression for all the self and mutual inductance in terms of θ

b) Determine and $L_d, L_q$ and $L_0$