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2 cot²(t ) sin(t ) - cot²(t ) = 0
cot²(t ) (2 sin(t ) - 1) = 0
cot²(t ) = 0 or 2 sin(t ) - 1 = 0
cot(t ) = 0 or sin(t ) = 1/2
cos(t ) / sin(t ) = 0 or sin(t ) = 1/2
cos(t ) = 0 or sin(t ) = 1/2
[t = cos⁻¹(0) + 2nπ or t = cos⁻¹(0) - π + 2nπ]
or [t = sin⁻¹(1/2) + 2nπ or t = π - sin⁻¹(1/2) + 2nπ]
(where n is any integer)
t = π/2 + 2nπ or t = -π/2 + 2nπ or t = π/6 + 2nπ or t = 5π/6 + 2nπ
Note that the first two families of solutions overlap and can be condensed, so that
t = π/2 + nπ or t = π/6 + 2nπ or t = 5π/6 + 2nπ