prove the following identity:

Secθ- 1/Secθ +1≡ Tan²(only the theta is divided by 2)θ/2

this is what i've done so far:

LHS =( secθ- 1)/ (secθ +1)

= (1/cosθ- 1)/(1/cosθ +1 )

=1- cosθ/ 1+ cosθ

from here, I don't know what to do next. help plz!!!