Given that tangent theta equals three halves comma pi less than theta less than StartFraction 3 pi Over 2 EndFraction commatanθ=32, π<θ<3π2, find the exact value of each of the following.
(a) sine left parenthesis 2 theta right parenthesissin(2θ)     
(b) cosine left parenthesis 2 theta right parenthesiscos(2θ)     
(c) sine StartFraction theta Over 2 EndFractionsinθ2     
(d) cosine StartFraction theta Over 2 EndFractioncosθ2     
(e) tangent left parenthesis 2 theta right parenthesistan(2θ)     
(f) tangent StartFraction theta Over 2 EndFractiontanθ2(a)  
sine left parenthesis 2 theta right parenthesissin(2θ)equals=nothing
(Type an exact answer, using radicals as needed.)