please give the answer in the python language

$4\mathrm{.}16[25]$ A $4R$ manipulator is shown schematically in Fig. $4\mathrm{.}15.$ The nonzero link

parameters are $a_1=1,{}_2=45,d_3=\sqrt[\phantom{2}]{2},$ and $a_3=\sqrt[\phantom{2}]{2},$ and the mechanism is

pictured in the configuration corresponding to $=[0,90,-90,0{]}^T.$ Each joint

has $+-180$ as limits$.$ Find all the values of ${}_3$ such that

${?}^0{P}_{4\text{O}\text{R}\text{G}}=[1\mathrm{.}12,1\mathrm{.}35,1\mathrm{.}2589{]}^T.$