Let p = tan2α - tanα and q = cotα - cot2α. What is (p+q) equal to?

p = tan2α - tanα = sin2α/cos2α - sinα/cosα = (sin2α·cosα - cos2α·sinα)/(cos2α·cosα) = sinα/(cos2α·cosα). q = cotα - cot2α = cosα/sinα - cos2α/sin2α = (cosα·sin2α - cos2α·sinα)/(sinα·sin2α) = sinα/(sinα·sin2α) = 1/sin2α... Computing carefully: p + q = sinα/(cosα·cos2α) + sinα/(sinα·sin2α). Using p·q = tan²α·... Actually p + q = 2/sin4α = 2cosec4α via standard identity.