Answer:

Explanation:
we would like to solve the following equation:

to do so we need to put the equation in term of a function of a angle therefore rewrite tanθ:

simplify multiplication:

cross multiplication:

isolate -3cosθ to left hand side and change its sign:

well we can rewrite sin²θ by applying Pythagorean theorem and that yields:

distribute:

now notice that our equation ended up with a pattern and that is Quadratic thus by letting cosθ be x to transform the equation:

rearrange it to standard form:

divide both sides by -1:

well we can factor the quadratic to do so rewrite -3x as -4x+x:

factor out 2x:

factor out 1:

group:

by Zero Product property we obtain:

cancel 1 from the first equation and add 2 to the e equation:

substitute back:

since cosθ is only defined for the interval [1,-1] the second equation is false for any value of θ but we can still continue the first equation

divide both sides by 2:

by unit circle we acquire:

add period of 2nπ:

for the interval [0,2π) θ is only defined when n is 0 Thus:

simplify:

hence,
θ is equal to 150° and 240°