Question

why it is necessary for theta to be a dimensionless quantity?

Answer 1

theta is the ratio of two similar quantities therefore it is a dimensionless quantity.

Answer 2

..not only θ...
..
All Angles are indeed dimensionless; the reason is that an angle is measured as the ratio of arc length to radius (meters per meter, say), which cancels out any units. Other angle measurements, such as degrees, are also dimensionless, though they are defined by different ratios, such as the ratio of the arc length to 1/360 of a circle, which results in the need for a multiplier. It is for this reason that we still need to name the unit, radians, rather than leaving it out entirely. Saying "radians" specifies the way in which the angle is measured; but it is still dimensionless and can be ignored as long as you know that radians are the correct method for the calculation being done.