Prove that the general solution of `tantheta=tanalpha` is given by : `theta=npi+alpha,n in Zdot`

Explanation

Given:
`tantheta=tanalpha`
`implies sintheta/costheta=sinalpha/cosalpha`
`implies sintheta/costheta-sinalpha/cosalpha=0`
Taking LCM
`implies(sinthetacosalpha-costhetasinalpha)/(costhetacosalpha)=0`
`implies sin(theta-alpha)/(costhetacosalpha)=0`
`implies sin(theta-alpha)=0`
`theta-alpha=npi` where, `npi in Z`
i.e. `n=(0,pm1,pm 2,pm 3---)`
`theta=npi+alpha`
Hence the general solution of `tantheta=tanalpha` is `theta=npi+alpha` where `n in Z`
i.e. `n=(0,pm 1, pm 2, pm 3,----)`