What is the canonical form based on sinus of the autoinduced EMF in a coil
I also found somewhere this formula regarding the EMF


Yes that's the correct formula and for a powered inductor the back (induced) emf it is Faraday's / Lenz's law: -

$$V = -L\dfrac{di}{dt}$$

So the induced (or back) emf is the mathematical differential of the current you have listed. This means the back emf is advanced by 90 degrees (then inverted by the minus sign) for a sinus driven coil thus your current of phase angle \$\pi/3\$ (or 60 degrees) is advanced to 150 degrees by the differentiation then inverted to -30 degrees by the minus sign.

Or just advance +60 degrees to -30.