@Vincen: Apologies for not replying sooner. The logs suggest that Insync is trying to connect using SSLv3. It is not supported by the server Insync is trying to connect to which causes the issue. Please try the following to debug.
Run openssl s_client -connect doc-00-7k-docs.googleusercontent.com:443 2>/dev/null | grep -C1 Protocol
. The output may look like this:
$ openssl s_client -connect doc-00-7k-docs.googleusercontent.com:443 2>/dev/null | grep -C1 Protocol
SSL-Session:
Protocol : TLSv1.2
Cipher : ECDHE-RSA-AES128-GCM-SHA256
This is just to confirm the protocol used when connecting normally.
Run the command nmap --script ssl-enum-ciphers -p 443 doc-00-7k-docs.googleusercontent.com
as well to confirm what protocols and ciphers are supported. In my test the output is:
$ nmap --script ssl-enum-ciphers -p 443 doc-00-7k-docs.googleusercontent.com
Starting Nmap 7.01 ( https://nmap.org ) at 2016-12-05 17:42 PHT
Nmap scan report for doc-00-7k-docs.googleusercontent.com (216.58.220.225)
Host is up (0.065s latency).
Other addresses for doc-00-7k-docs.googleusercontent.com (not scanned): 2404:6800:4004:81a::2001
rDNS record for 216.58.220.225: nrt13s37-in-f225.1e100.net
PORT STATE SERVICE
443/tcp open https
| ssl-enum-ciphers:
| TLSv1.0:
| ciphers:
| TLS_ECDHE_ECDSA_WITH_AES_128_CBC_SHA (secp256r1) - A
| TLS_ECDHE_ECDSA_WITH_AES_256_CBC_SHA (secp256r1) - A
| TLS_ECDHE_RSA_WITH_AES_128_CBC_SHA (secp256r1) - A
| TLS_RSA_WITH_AES_128_CBC_SHA (rsa 2048) - A
| TLS_RSA_WITH_3DES_EDE_CBC_SHA (rsa 2048) - C
| TLS_ECDHE_RSA_WITH_AES_256_CBC_SHA (secp256r1) - A
| TLS_RSA_WITH_AES_256_CBC_SHA (rsa 2048) - A
| compressors:
| NULL
| cipher preference: server
| TLSv1.1:
| ciphers:
| TLS_ECDHE_ECDSA_WITH_AES_128_CBC_SHA (secp256r1) - A
| TLS_ECDHE_ECDSA_WITH_AES_256_CBC_SHA (secp256r1) - A
| TLS_ECDHE_RSA_WITH_AES_128_CBC_SHA (secp256r1) - A
| TLS_RSA_WITH_AES_128_CBC_SHA (rsa 2048) - A
| TLS_RSA_WITH_3DES_EDE_CBC_SHA (rsa 2048) - C
| TLS_ECDHE_RSA_WITH_AES_256_CBC_SHA (secp256r1) - A
| TLS_RSA_WITH_AES_256_CBC_SHA (rsa 2048) - A
| compressors:
| NULL
| cipher preference: server
| TLSv1.2:
| ciphers:
| TLS_ECDHE_ECDSA_WITH_AES_128_GCM_SHA256 (secp256r1) - A
| TLS_ECDHE_ECDSA_WITH_CHACHA20_POLY1305_SHA256 (secp256r1) - A
| TLS_ECDHE_ECDSA_WITH_AES_128_CBC_SHA (secp256r1) - A
| TLS_ECDHE_ECDSA_WITH_AES_256_GCM_SHA384 (secp256r1) - A
| TLS_ECDHE_ECDSA_WITH_AES_128_CBC_SHA256 (secp256r1) - A
| TLS_ECDHE_ECDSA_WITH_AES_256_CBC_SHA (secp256r1) - A
| TLS_ECDHE_ECDSA_WITH_AES_256_CBC_SHA384 (secp256r1) - A
| TLS_ECDHE_RSA_WITH_AES_128_GCM_SHA256 (secp256r1) - A
| TLS_ECDHE_RSA_WITH_CHACHA20_POLY1305_SHA256 (secp256r1) - A
| TLS_ECDHE_RSA_WITH_AES_128_CBC_SHA (secp256r1) - A
| TLS_RSA_WITH_AES_128_GCM_SHA256 (rsa 2048) - A
| TLS_RSA_WITH_AES_128_CBC_SHA (rsa 2048) - A
| TLS_RSA_WITH_AES_128_CBC_SHA256 (rsa 2048) - A
| TLS_RSA_WITH_3DES_EDE_CBC_SHA (rsa 2048) - C
| TLS_ECDHE_RSA_WITH_AES_256_GCM_SHA384 (secp256r1) - A
| TLS_ECDHE_RSA_WITH_AES_128_CBC_SHA256 (secp256r1) - A
| TLS_ECDHE_RSA_WITH_AES_256_CBC_SHA (secp256r1) - A
| TLS_ECDHE_RSA_WITH_AES_256_CBC_SHA384 (secp256r1) - A
| TLS_RSA_WITH_AES_256_GCM_SHA384 (rsa 2048) - A
| TLS_RSA_WITH_AES_256_CBC_SHA (rsa 2048) - A
| TLS_RSA_WITH_AES_256_CBC_SHA256 (rsa 2048) - A
| compressors:
| NULL
| cipher preference: server
|_ least strength: C
Nmap done: 1 IP address (1 host up) scanned in 10.38 seconds
which confirms that the server only supports TLS.