cosΘ - tanΘ =0 add tanΘ to both sides
cosΘ = tanΘ
The easiest way to solve this - IMHO - is with a graph.......here it is....
https://www.desmos.com/calculator/wvqydtk4mt
The points of intersection occur at about 38.2° and at about 141.8°
And converting to rads we have ....about .6667 rads and about 2.475 rads on (0, 2pi)