1 способ
cos a=1/2
a=+-π/3+2πk k∈Z
т.к. а∈(π; 3π/2)
а=5π/3
tg a/2=tg 5π/6=-√3/3

2 способ
tg a/2=(1-cosa)/sina
IsinaI=√(1-cos²a)=√(1-1/4)=√3/2
т.к. х∈(π; 3π/2)
sina=-√3/2
tg a/2=(1-1/2)/(-√3/2)=-1/2: √3/2=-1/√3=-√3/3