$\frac{\left(\cos(\theta )+i\sin(\theta )\right)^{15}}{\left(\cos(\theta )-i\sin(\theta )\right)^{34}}$

$\frac{455i\left(\sin(\theta )\right)^{3}\left(\cos(\theta )\right)^{12}+1365i\left(\cos(\theta )\right)^{4}\left(\sin(\theta )\right)^{11}+6435i\left(\sin(\theta )\right)^{7}\left(\cos(\theta )\right)^{8}-105i\left(\cos(\theta )\right)^{2}\left(\sin(\theta )\right)^{13}-3003i\left(\sin(\theta )\right)^{5}\left(\cos(\theta )\right)^{10}-5005i\left(\cos(\theta )\right)^{6}\left(\sin(\theta )\right)^{9}-15i\sin(\theta )\left(\cos(\theta )\right)^{14}+105\left(\sin(\theta )\right)^{2}\left(\cos(\theta )\right)^{13}+3003\left(\cos(\theta )\right)^{5}\left(\sin(\theta )\right)^{10}+5005\left(\sin(\theta )\right)^{6}\left(\cos(\theta )\right)^{9}-455\left(\cos(\theta )\right)^{3}\left(\sin(\theta )\right)^{12}-1365\left(\sin(\theta )\right)^{4}\left(\cos(\theta )\right)^{11}-6435\left(\cos(\theta )\right)^{7}\left(\sin(\theta )\right)^{8}+15\cos(\theta )\left(\sin(\theta )\right)^{14}+i\left(\sin(\theta )\right)^{15}-\left(\cos(\theta )\right)^{15}}{\left(i\sin(2\theta )-\cos(2\theta )\right)^{17}}$