Consider the space curve given by the equation

r(t)=t^2i +[sin(2t)-2tcos(2t)]j+[cos(2t)+2tsin(2t)]k

(a) Find the unit tangent vector T(t) and the equation of the tangent line at t=Pi.

Everytime I attempt this problem I end up with the most despicable derivatives. I have tried to use trigonometric identities to clean up the problem I'm trying to solve a bit but it still leads to unatural results (a huge repetitive derivative computation). Is there some trigonometric identity that I'm missing out on or a trick that could produce results that make sense?