complex values and residuee theorem

I have two questions, I have tried to find stuff on them but failed

(1) find all complex values z such that e^(z+2)=1+i

I tried to put z=log(1+i)-2 but dont think thats not right

(2)use the residue theorem to evaluate

integralc(tanz)dz where c is the positively orientated circle |z|=2

i thought with the residue theorem you had to have a fraction so you could set the bottom to zero and get a singularity. I thought you could change tanz into sinz/cosz and set cosz to zero. but thats wrong

any help appreciated on either question

thanks :)