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q. ln(i)

This question came up in an exam i had today.. dont think i answered it correctly though!

i went for the euler relation:

e^i*θ = cos(θ) + i*sin(θ)

next i set θ = 1 and found the natural log of the equation twice

ln(i) = ln(ln(cos(1) + i*sin(1)))

My calculator wasn't good enough to work this out without returning a math error, so i left it in that form (except i think i calculated the trig functions)

Can anyone shine some light on this problem?