Solve 2 sin 20 - tan 20 = 0 for 0 in [0°, 360°).

Any help would be really appreciated!

Step-by-step explanation:

If there is a character you cannot type, such as θ, you are better off substituting a different letter, or describing it in words. For example, write it as "sinA" or "sin(theta)"

Never use 0 as a substitute for θ! 0 is a constant with a specific value.

Since the argument of the trig functions is an expression, you should put parentheses around it:  sin(2A).

I used several trigonometric identities for this question:

Double-angle formula for sine: sin(2θ) = 2sinθcosθ

Double-angle formula for tangent: tan(2θ) = 2tanθ/(1-tan²θ)

Quotient identity: tanθ = sinθ/cosθ 

Reciprocal identity: secθ = 1/cosθ

Pythagorean identity: 1+tan²θ = sec²θ

2sin(2θ) - tan(2θ) = 0

2sin(2θ) = tan(2θ)

2·2sinθcosθ = 2tanθ/(1-tan²θ)

2sinθcosθ = tanθ/(1-tan²θ)

2sinθcosθ = (sinθ/cosθ ) · 1/(cosθ(1-tan²θ))

2(1-tan²θ) = 1/cos²θ

2(1-tan²θ) = sec²θ

2-2tan²θ) = 1+tan²θ

1 = 3tan²θ

tan²θ = ⅓

tanθ = ±1/√3

θ = 30°, 330°

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