You just have to differentiate the
y=yinitial + x (tantheta) - [(gx^2)/(2(vinitial^2)(cos^2theta))]
with respect to theta.
Then you will arrive at the last line.
Remember that differentiating with respect to theta here means y_initial is constant, and x is constant too.
Of course the g and the V_initial are constants also.
Why not write V_initial as Vo, Y_initial as Yo?