Final answer:
The question appears to refer to trigonometry and requires using the tangent subtraction formula, though there is an error in the question. The proof process involves verifying identities, simplifying expressions, and ensuring angles are in the correct quadrant. Reasonableness checks and context-specific equations might also be necessary.
Step-by-step explanation:
To review the steps of the proof for τ(π/4 - 8), we must first recognize that this appears to be an attempt to use the tangent subtraction formula, which is τ(α - β) = (τα - τβ)/(1 + τα·τβ), though the given question seems to have an error. Typically, these types of formulas are used to simplify the expressions of trigonometric functions of compound angles.
However, the proof process for tangents of specific angles involves establishing identities and checking against known values, such as τ(π/4) = 1 and the periodicity of the tangent function. Without the exact context or correct expression, it is difficult to provide a complete response, but reviewing the proof would include verifying each step against known identities, simplifying expressions, and ensuring the relevance of the calculated angle to the problem, such as making sure the angle is in the correct quadrant.
Checking for reasonableness involves verifying signs and consistency with any provided figures or sketches. One might also need to solve equations for variables in context-specific formulas, as indicated by the mention of m1, m2, θ1, and θ2 in the provided reference information.