The value of cot⁡θ−tan⁡θ−2tan⁡2θ−4tan⁡4θ−8cot⁡8θ is

We know that∴ cot⁡α−tan⁡α=2cot⁡2αcot⁡θ−tan⁡θ−2tan⁡2θ−4tan⁡4θ−8cot⁡8θ=2cot⁡2θ−2tan⁡2θ−4tan⁡4θ−8cot⁡8θ=2(2cot⁡4θ)−4tan⁡4θ−8cot⁡8θ=4cot⁡4θ−4tan⁡4θ−8cot⁡8θ=4(cot⁡4θ−tan⁡40)−8cot⁡8θ=4×2cot⁡8θ−8cot⁡8θ=0